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String Topology and Cyclic Homology
Ralph L. Cohen Kathryn Hess Alexander A. Voronov
Resumen/Descripción – provisto por la editorial
No disponible.
Palabras clave – provistas por la editorial
Algebraic Topology; Manifolds and Cell Complexes (incl. Diff.Topology); Mathematical Methods in Physics
Disponibilidad
Institución detectada | Año de publicación | Navegá | Descargá | Solicitá |
---|---|---|---|---|
No detectada | 2006 | SpringerLink |
Información
Tipo de recurso:
libros
ISBN impreso
978-3-7643-2182-6
ISBN electrónico
978-3-7643-7388-7
Editor responsable
Springer Nature
País de edición
Reino Unido
Fecha de publicación
2006
Información sobre derechos de publicación
© Birkhäuser Verlag 2006
Cobertura temática
Tabla de contenidos
Introduction
Ralph L. Cohen; Kathryn Hess; Alexander A. Voronov
The origin of the Moon 4.56 Gyr ago, its subsequent evolution, and the implications of both relative to the Earth remain subject to lively debate. Because the internal geochemistry and geophysics of the Moon does not appear consistent with an origin by the giant impact of a Mars-sized asteroid on the Earth, this hypothesis is challenged by one that proposes the capture of an independently formed planetesimal. The Moon—s internal structure also indicates that it and all the terrestrial planets initially had relatively cool, chondritic proto-cores prior to formation of metallic cores. Evidence exists that these proto-cores delayed formation of metallic cores for periods that correlate with the final mass of a planet.
The impact history of the inner solar system has been broadly outlined by the modern investigation of the Moon. First, soon after the formation of a coherent lunar crust and against an intense background of smaller cratering events, the Moon was subjected to extremely large impacts that formed basins up to 3200km in diameter. On Earth, the melt sheets from these continental-scale impacts may have been responsible for the formation of the first continental crust at ∼4.4 Gyr. Second, ∼50 impact basins >300 km in diameter formed between 4.5 and 3.8 Gyr probably by pulses of impactors produced during the migration and interaction of the giant planets within a structured solar disk of planetesimal rings. The last of these pulses at about 3.85 Gyr, producing the ∼14 mascon basins, resurfaced most of the Moon, and suggested an apparent “cataclysm” at that time. This period of 700 Myr may have been one of “punctuated cataclysm” as one or more giant planets encountered separate planetesimal rings and gaps during outward orbital migration. Finally, the implication of this violent impact history in the inner solar system prior to 3.8 Gyr relative to the surfaces of the hydrous terrestrial planets, that is, Earth, Mars and probably early Venus, is that clays were the dominant mineral species. These clays, as well as volcanic sulfides, may have provided the templates for the formation of complex organic precursors that made up the first living cells.
Part I - Notes on String Topology | Pp. 3-4
Intersection theory in loop spaces
Ralph L. Cohen; Kathryn Hess; Alexander A. Voronov
The origin of the Moon 4.56 Gyr ago, its subsequent evolution, and the implications of both relative to the Earth remain subject to lively debate. Because the internal geochemistry and geophysics of the Moon does not appear consistent with an origin by the giant impact of a Mars-sized asteroid on the Earth, this hypothesis is challenged by one that proposes the capture of an independently formed planetesimal. The Moon—s internal structure also indicates that it and all the terrestrial planets initially had relatively cool, chondritic proto-cores prior to formation of metallic cores. Evidence exists that these proto-cores delayed formation of metallic cores for periods that correlate with the final mass of a planet.
The impact history of the inner solar system has been broadly outlined by the modern investigation of the Moon. First, soon after the formation of a coherent lunar crust and against an intense background of smaller cratering events, the Moon was subjected to extremely large impacts that formed basins up to 3200km in diameter. On Earth, the melt sheets from these continental-scale impacts may have been responsible for the formation of the first continental crust at ∼4.4 Gyr. Second, ∼50 impact basins >300 km in diameter formed between 4.5 and 3.8 Gyr probably by pulses of impactors produced during the migration and interaction of the giant planets within a structured solar disk of planetesimal rings. The last of these pulses at about 3.85 Gyr, producing the ∼14 mascon basins, resurfaced most of the Moon, and suggested an apparent “cataclysm” at that time. This period of 700 Myr may have been one of “punctuated cataclysm” as one or more giant planets encountered separate planetesimal rings and gaps during outward orbital migration. Finally, the implication of this violent impact history in the inner solar system prior to 3.8 Gyr relative to the surfaces of the hydrous terrestrial planets, that is, Earth, Mars and probably early Venus, is that clays were the dominant mineral species. These clays, as well as volcanic sulfides, may have provided the templates for the formation of complex organic precursors that made up the first living cells.
Part I - Notes on String Topology | Pp. 5-23
The cacti operad
Ralph L. Cohen; Kathryn Hess; Alexander A. Voronov
The origin of the Moon 4.56 Gyr ago, its subsequent evolution, and the implications of both relative to the Earth remain subject to lively debate. Because the internal geochemistry and geophysics of the Moon does not appear consistent with an origin by the giant impact of a Mars-sized asteroid on the Earth, this hypothesis is challenged by one that proposes the capture of an independently formed planetesimal. The Moon—s internal structure also indicates that it and all the terrestrial planets initially had relatively cool, chondritic proto-cores prior to formation of metallic cores. Evidence exists that these proto-cores delayed formation of metallic cores for periods that correlate with the final mass of a planet.
The impact history of the inner solar system has been broadly outlined by the modern investigation of the Moon. First, soon after the formation of a coherent lunar crust and against an intense background of smaller cratering events, the Moon was subjected to extremely large impacts that formed basins up to 3200km in diameter. On Earth, the melt sheets from these continental-scale impacts may have been responsible for the formation of the first continental crust at ∼4.4 Gyr. Second, ∼50 impact basins >300 km in diameter formed between 4.5 and 3.8 Gyr probably by pulses of impactors produced during the migration and interaction of the giant planets within a structured solar disk of planetesimal rings. The last of these pulses at about 3.85 Gyr, producing the ∼14 mascon basins, resurfaced most of the Moon, and suggested an apparent “cataclysm” at that time. This period of 700 Myr may have been one of “punctuated cataclysm” as one or more giant planets encountered separate planetesimal rings and gaps during outward orbital migration. Finally, the implication of this violent impact history in the inner solar system prior to 3.8 Gyr relative to the surfaces of the hydrous terrestrial planets, that is, Earth, Mars and probably early Venus, is that clays were the dominant mineral species. These clays, as well as volcanic sulfides, may have provided the templates for the formation of complex organic precursors that made up the first living cells.
Part I - Notes on String Topology | Pp. 25-45
Field theoretic properties of string topology
Ralph L. Cohen; Kathryn Hess; Alexander A. Voronov
The origin of the Moon 4.56 Gyr ago, its subsequent evolution, and the implications of both relative to the Earth remain subject to lively debate. Because the internal geochemistry and geophysics of the Moon does not appear consistent with an origin by the giant impact of a Mars-sized asteroid on the Earth, this hypothesis is challenged by one that proposes the capture of an independently formed planetesimal. The Moon—s internal structure also indicates that it and all the terrestrial planets initially had relatively cool, chondritic proto-cores prior to formation of metallic cores. Evidence exists that these proto-cores delayed formation of metallic cores for periods that correlate with the final mass of a planet.
The impact history of the inner solar system has been broadly outlined by the modern investigation of the Moon. First, soon after the formation of a coherent lunar crust and against an intense background of smaller cratering events, the Moon was subjected to extremely large impacts that formed basins up to 3200km in diameter. On Earth, the melt sheets from these continental-scale impacts may have been responsible for the formation of the first continental crust at ∼4.4 Gyr. Second, ∼50 impact basins >300 km in diameter formed between 4.5 and 3.8 Gyr probably by pulses of impactors produced during the migration and interaction of the giant planets within a structured solar disk of planetesimal rings. The last of these pulses at about 3.85 Gyr, producing the ∼14 mascon basins, resurfaced most of the Moon, and suggested an apparent “cataclysm” at that time. This period of 700 Myr may have been one of “punctuated cataclysm” as one or more giant planets encountered separate planetesimal rings and gaps during outward orbital migration. Finally, the implication of this violent impact history in the inner solar system prior to 3.8 Gyr relative to the surfaces of the hydrous terrestrial planets, that is, Earth, Mars and probably early Venus, is that clays were the dominant mineral species. These clays, as well as volcanic sulfides, may have provided the templates for the formation of complex organic precursors that made up the first living cells.
Part I - Notes on String Topology | Pp. 47-65
A Morse theoretic viewpoint
Ralph L. Cohen; Kathryn Hess; Alexander A. Voronov
The origin of the Moon 4.56 Gyr ago, its subsequent evolution, and the implications of both relative to the Earth remain subject to lively debate. Because the internal geochemistry and geophysics of the Moon does not appear consistent with an origin by the giant impact of a Mars-sized asteroid on the Earth, this hypothesis is challenged by one that proposes the capture of an independently formed planetesimal. The Moon—s internal structure also indicates that it and all the terrestrial planets initially had relatively cool, chondritic proto-cores prior to formation of metallic cores. Evidence exists that these proto-cores delayed formation of metallic cores for periods that correlate with the final mass of a planet.
The impact history of the inner solar system has been broadly outlined by the modern investigation of the Moon. First, soon after the formation of a coherent lunar crust and against an intense background of smaller cratering events, the Moon was subjected to extremely large impacts that formed basins up to 3200km in diameter. On Earth, the melt sheets from these continental-scale impacts may have been responsible for the formation of the first continental crust at ∼4.4 Gyr. Second, ∼50 impact basins >300 km in diameter formed between 4.5 and 3.8 Gyr probably by pulses of impactors produced during the migration and interaction of the giant planets within a structured solar disk of planetesimal rings. The last of these pulses at about 3.85 Gyr, producing the ∼14 mascon basins, resurfaced most of the Moon, and suggested an apparent “cataclysm” at that time. This period of 700 Myr may have been one of “punctuated cataclysm” as one or more giant planets encountered separate planetesimal rings and gaps during outward orbital migration. Finally, the implication of this violent impact history in the inner solar system prior to 3.8 Gyr relative to the surfaces of the hydrous terrestrial planets, that is, Earth, Mars and probably early Venus, is that clays were the dominant mineral species. These clays, as well as volcanic sulfides, may have provided the templates for the formation of complex organic precursors that made up the first living cells.
Part I - Notes on String Topology | Pp. 67-77
Brane topology
Ralph L. Cohen; Kathryn Hess; Alexander A. Voronov
The origin of the Moon 4.56 Gyr ago, its subsequent evolution, and the implications of both relative to the Earth remain subject to lively debate. Because the internal geochemistry and geophysics of the Moon does not appear consistent with an origin by the giant impact of a Mars-sized asteroid on the Earth, this hypothesis is challenged by one that proposes the capture of an independently formed planetesimal. The Moon—s internal structure also indicates that it and all the terrestrial planets initially had relatively cool, chondritic proto-cores prior to formation of metallic cores. Evidence exists that these proto-cores delayed formation of metallic cores for periods that correlate with the final mass of a planet.
The impact history of the inner solar system has been broadly outlined by the modern investigation of the Moon. First, soon after the formation of a coherent lunar crust and against an intense background of smaller cratering events, the Moon was subjected to extremely large impacts that formed basins up to 3200km in diameter. On Earth, the melt sheets from these continental-scale impacts may have been responsible for the formation of the first continental crust at ∼4.4 Gyr. Second, ∼50 impact basins >300 km in diameter formed between 4.5 and 3.8 Gyr probably by pulses of impactors produced during the migration and interaction of the giant planets within a structured solar disk of planetesimal rings. The last of these pulses at about 3.85 Gyr, producing the ∼14 mascon basins, resurfaced most of the Moon, and suggested an apparent “cataclysm” at that time. This period of 700 Myr may have been one of “punctuated cataclysm” as one or more giant planets encountered separate planetesimal rings and gaps during outward orbital migration. Finally, the implication of this violent impact history in the inner solar system prior to 3.8 Gyr relative to the surfaces of the hydrous terrestrial planets, that is, Earth, Mars and probably early Venus, is that clays were the dominant mineral species. These clays, as well as volcanic sulfides, may have provided the templates for the formation of complex organic precursors that made up the first living cells.
Part I - Notes on String Topology | Pp. 79-87
Preliminaries
Ralph L. Cohen; Kathryn Hess; Alexander A. Voronov
The origin of the Moon 4.56 Gyr ago, its subsequent evolution, and the implications of both relative to the Earth remain subject to lively debate. Because the internal geochemistry and geophysics of the Moon does not appear consistent with an origin by the giant impact of a Mars-sized asteroid on the Earth, this hypothesis is challenged by one that proposes the capture of an independently formed planetesimal. The Moon—s internal structure also indicates that it and all the terrestrial planets initially had relatively cool, chondritic proto-cores prior to formation of metallic cores. Evidence exists that these proto-cores delayed formation of metallic cores for periods that correlate with the final mass of a planet.
The impact history of the inner solar system has been broadly outlined by the modern investigation of the Moon. First, soon after the formation of a coherent lunar crust and against an intense background of smaller cratering events, the Moon was subjected to extremely large impacts that formed basins up to 3200km in diameter. On Earth, the melt sheets from these continental-scale impacts may have been responsible for the formation of the first continental crust at ∼4.4 Gyr. Second, ∼50 impact basins >300 km in diameter formed between 4.5 and 3.8 Gyr probably by pulses of impactors produced during the migration and interaction of the giant planets within a structured solar disk of planetesimal rings. The last of these pulses at about 3.85 Gyr, producing the ∼14 mascon basins, resurfaced most of the Moon, and suggested an apparent “cataclysm” at that time. This period of 700 Myr may have been one of “punctuated cataclysm” as one or more giant planets encountered separate planetesimal rings and gaps during outward orbital migration. Finally, the implication of this violent impact history in the inner solar system prior to 3.8 Gyr relative to the surfaces of the hydrous terrestrial planets, that is, Earth, Mars and probably early Venus, is that clays were the dominant mineral species. These clays, as well as volcanic sulfides, may have provided the templates for the formation of complex organic precursors that made up the first living cells.
Part II - An Algebraic Model for Mod 2 Topological Cyclic Homology | Pp. 103-113
Free loop spaces
Ralph L. Cohen; Kathryn Hess; Alexander A. Voronov
The origin of the Moon 4.56 Gyr ago, its subsequent evolution, and the implications of both relative to the Earth remain subject to lively debate. Because the internal geochemistry and geophysics of the Moon does not appear consistent with an origin by the giant impact of a Mars-sized asteroid on the Earth, this hypothesis is challenged by one that proposes the capture of an independently formed planetesimal. The Moon—s internal structure also indicates that it and all the terrestrial planets initially had relatively cool, chondritic proto-cores prior to formation of metallic cores. Evidence exists that these proto-cores delayed formation of metallic cores for periods that correlate with the final mass of a planet.
The impact history of the inner solar system has been broadly outlined by the modern investigation of the Moon. First, soon after the formation of a coherent lunar crust and against an intense background of smaller cratering events, the Moon was subjected to extremely large impacts that formed basins up to 3200km in diameter. On Earth, the melt sheets from these continental-scale impacts may have been responsible for the formation of the first continental crust at ∼4.4 Gyr. Second, ∼50 impact basins >300 km in diameter formed between 4.5 and 3.8 Gyr probably by pulses of impactors produced during the migration and interaction of the giant planets within a structured solar disk of planetesimal rings. The last of these pulses at about 3.85 Gyr, producing the ∼14 mascon basins, resurfaced most of the Moon, and suggested an apparent “cataclysm” at that time. This period of 700 Myr may have been one of “punctuated cataclysm” as one or more giant planets encountered separate planetesimal rings and gaps during outward orbital migration. Finally, the implication of this violent impact history in the inner solar system prior to 3.8 Gyr relative to the surfaces of the hydrous terrestrial planets, that is, Earth, Mars and probably early Venus, is that clays were the dominant mineral species. These clays, as well as volcanic sulfides, may have provided the templates for the formation of complex organic precursors that made up the first living cells.
Part II - An Algebraic Model for Mod 2 Topological Cyclic Homology | Pp. 115-137
Homotopy orbit spaces
Ralph L. Cohen; Kathryn Hess; Alexander A. Voronov
The origin of the Moon 4.56 Gyr ago, its subsequent evolution, and the implications of both relative to the Earth remain subject to lively debate. Because the internal geochemistry and geophysics of the Moon does not appear consistent with an origin by the giant impact of a Mars-sized asteroid on the Earth, this hypothesis is challenged by one that proposes the capture of an independently formed planetesimal. The Moon—s internal structure also indicates that it and all the terrestrial planets initially had relatively cool, chondritic proto-cores prior to formation of metallic cores. Evidence exists that these proto-cores delayed formation of metallic cores for periods that correlate with the final mass of a planet.
The impact history of the inner solar system has been broadly outlined by the modern investigation of the Moon. First, soon after the formation of a coherent lunar crust and against an intense background of smaller cratering events, the Moon was subjected to extremely large impacts that formed basins up to 3200km in diameter. On Earth, the melt sheets from these continental-scale impacts may have been responsible for the formation of the first continental crust at ∼4.4 Gyr. Second, ∼50 impact basins >300 km in diameter formed between 4.5 and 3.8 Gyr probably by pulses of impactors produced during the migration and interaction of the giant planets within a structured solar disk of planetesimal rings. The last of these pulses at about 3.85 Gyr, producing the ∼14 mascon basins, resurfaced most of the Moon, and suggested an apparent “cataclysm” at that time. This period of 700 Myr may have been one of “punctuated cataclysm” as one or more giant planets encountered separate planetesimal rings and gaps during outward orbital migration. Finally, the implication of this violent impact history in the inner solar system prior to 3.8 Gyr relative to the surfaces of the hydrous terrestrial planets, that is, Earth, Mars and probably early Venus, is that clays were the dominant mineral species. These clays, as well as volcanic sulfides, may have provided the templates for the formation of complex organic precursors that made up the first living cells.
Part II - An Algebraic Model for Mod 2 Topological Cyclic Homology | Pp. 139-151
A model for mod 2 topological cyclic homology
Ralph L. Cohen; Kathryn Hess; Alexander A. Voronov
The origin of the Moon 4.56 Gyr ago, its subsequent evolution, and the implications of both relative to the Earth remain subject to lively debate. Because the internal geochemistry and geophysics of the Moon does not appear consistent with an origin by the giant impact of a Mars-sized asteroid on the Earth, this hypothesis is challenged by one that proposes the capture of an independently formed planetesimal. The Moon—s internal structure also indicates that it and all the terrestrial planets initially had relatively cool, chondritic proto-cores prior to formation of metallic cores. Evidence exists that these proto-cores delayed formation of metallic cores for periods that correlate with the final mass of a planet.
The impact history of the inner solar system has been broadly outlined by the modern investigation of the Moon. First, soon after the formation of a coherent lunar crust and against an intense background of smaller cratering events, the Moon was subjected to extremely large impacts that formed basins up to 3200km in diameter. On Earth, the melt sheets from these continental-scale impacts may have been responsible for the formation of the first continental crust at ∼4.4 Gyr. Second, ∼50 impact basins >300 km in diameter formed between 4.5 and 3.8 Gyr probably by pulses of impactors produced during the migration and interaction of the giant planets within a structured solar disk of planetesimal rings. The last of these pulses at about 3.85 Gyr, producing the ∼14 mascon basins, resurfaced most of the Moon, and suggested an apparent “cataclysm” at that time. This period of 700 Myr may have been one of “punctuated cataclysm” as one or more giant planets encountered separate planetesimal rings and gaps during outward orbital migration. Finally, the implication of this violent impact history in the inner solar system prior to 3.8 Gyr relative to the surfaces of the hydrous terrestrial planets, that is, Earth, Mars and probably early Venus, is that clays were the dominant mineral species. These clays, as well as volcanic sulfides, may have provided the templates for the formation of complex organic precursors that made up the first living cells.
Part II - An Algebraic Model for Mod 2 Topological Cyclic Homology | Pp. 153-159