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1.

図書

図書
Victor W. Guillemin, Shlomo Sternberg
出版情報: Berlin : Springer, 1999  xxiii, 228 p. ; 25 cm
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Introduction
Equivariant Cohomology in Topology / 1:
Equivariant Cohomology via Classifying Bundles / 1.1:
Existence of Classifying Spaces / 1.2:
Bibliographical Notes for Chapter 1 / 1.3:
G* Modules / 2:
Differential-Geometric Identities / 2.1:
The Language of Superalgebra / 2.2:
From Geometry to Algebra / 2.3:
Cohomology / 2.3.1:
Acyclicity / 2.3.2:
Chain Homotopies / 2.3.3:
Free Actions and the Condition (C) / 2.3.4:
The Basic Subcomplex / 2.3.5:
Equivariant Cohomology of G* Algebras / 2.4:
The Equivariant de Rham Theorem / 2.5:
Bibliographical Notes for Chapter 2 / 2.6:
The Weil Algebra / 3:
The Koszul Complex / 3.1:
Classifying Maps / 3.2:
W* Modules / 3.4:
Bibliographical Notes for Chapter 3 / 3.5:
The Weil Model and the Cartan Model / 4:
The Mathai-Quillen Isomorphism / 4.1:
The Cartan Model / 4.2:
Equivariant Cohomology of W* Modules / 4.3:
H ((A ⊗ E)bas) does not depend on E / 4.4:
The Characteristic Homomorphism / 4.5:
Commuting Actions / 4.6:
The Equivariant Cohomology of Homogeneous Spaces / 4.7:
Exact Sequences / 4.8:
Bibliographical Notes for Chapter 4 / 4.9:
Cartan's Formula / 5:
The Cartan Model for W* Modules / 5.1:
Bibliographical Notes for Chapter 5 / 5.2:
Spectral Sequences / 6:
Spectral Sequences of Double Complexes / 6.1:
The First Term / 6.2:
The Long Exact Sequence / 6.3:
Useful Facts for Doing Computations / 6.4:
Functorial Behavior / 6.4.1:
Gaps / 6.4.2:
Switching Rows and Columns / 6.4.3:
The Cartan Model as a Double Complex
HG(A) as an S(g*)G-Module
Morphisms of G* Modules
Restricting the Group
Bibliographical Notes for Chapter 6 / 6.5:
Fermionic Integration / 7:
Definition and Elementary Properties / 7.1:
Integration by Parts / 7.1.1:
Change of Variables / 7.1.2:
Gaussian Integrals / 7.1.3:
Iterated Integrals / 7.1.4:
The Fourier Transform / 7.1.5:
The Mathai-Quillen Construction
The Fourier Transform of the Koszul Complex / 7.2:
Bibliographical Notes for Chapter 7 / 7.3:
Characteristic Classes / 8:
Vector Bundles / 8.1:
The Invariants / 8.2:
G = U(n) / 8.2.1:
G = O(n) / 8.2.2:
G = SO(2n) / 8.2.3:
Relations Between the Invariants / 8.3:
Restriction from U(n) to O(n) / 8.3.1:
Restriction from SO(2n) to U(n) / 8.3.2:
Restriction from U(n) to U(k) × U(ℓ) / 8.3.3:
Symplectic Vector Bundles / 8.4:
Consistent Complex Structures / 8.4.1:
Characteristic Classes of Symplectic Vector Bundles / 8.4.2:
Equivariant Characteristic Classes / 8.5:
Equivariant Chern classes / 8.5.1:
Equivariant Characteristic Classes of a Vector Bundle Over a Point / 8.5.2:
Equivariant Characteristic Classes as Fixed Point Data / 8.5.3:
The Splitting Principle in Topology
Bibliographical Notes for Chapter 8
Equivariant Symplectic Forms / 9:
Equivariantly Closed Two-Forms / 9.1:
The Case M = G / 9.2:
Equivariantly Closed Two-Forms on Homogeneous Spaces / 9.3:
The Compact Case / 9.4:
Minimal Coupling / 9.5:
Symplectic Reduction / 9.6:
The Duistermaat-Heckman Theorem / 9.7:
The Cohomology Ring of Reduced Spaces / 9.8:
Flag Manifolds / 9.8.1:
Delzant Spaces / 9.8.2:
Reduction: The Linear Case / 9.8.3:
Equivariant Duistermaat-Heckman
Group Valued Moment Maps
The Canonical Equivariant Closed Three-Form on G / 9.10.1:
The Exponential Map / 9.10.2:
G-Valued Moment Maps on Hamiltonian G-Manifolds / 9.10.3:
Conjugacy Classes / 9.10.4:
Bibliographical Notes for Chapter 9 / 9.11:
The Thom Class and Localization / 10:
Fiber Integration of Equivariant Forms / 10.1:
The Equivariant Normal Bundle / 10.2:
Modifying ν / 10.3:
Verifying that τ is a Thom Form / 10.4:
The Thom Class and the Euler Class / 10.5:
The Fiber Integral on Cohomology / 10.6:
Push-Forward in General / 10.7:
Localization / 10.8:
The Localization for Torus Actions / 10.9:
Bibliographical Notes for Chapter 10 / 10.10:
The Abstract Localization Theorem / 11:
Relative Equivariant de Rham Theory / 11.1:
Mayer-Vietoris / 11.2:
S(g*) Modules / 11.3:
The Chang-Skjelbred Theorem / 11.4:
Some Consequences of Equivariant Formality / 11.6:
Two Dimensional G-Manifolds / 11.7:
A Theorem of Goresky-Kottwitz-Mac Pherson / 11.8:
Bibliographical Notes for Chapter 11 / 11.9:
Appendix
Notions d'algèbre différentielle; application aux groupes de Lie et aux variétés où opère un groupe de Lie / Henri Cartan
La transgression dans un groupe de Lie et dans un espace fibré principal
Bibliography
Index
Introduction
Equivariant Cohomology in Topology / 1:
Equivariant Cohomology via Classifying Bundles / 1.1:
2.

図書

図書
Jean-Louis Loday
出版情報: Berlin ; New York : Springer-Verlag, c1998  xviii, 513 p. ; 25 cm
シリーズ名: Die Grundlehren der mathematischen Wissenschaften ; 301
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3.

図書

図書
Joachim Kock, Israel Vainsencher
出版情報: Boston : Birkhäuser, c2007  xii, 159 p. ; 25 cm
シリーズ名: Progress in mathematics ; v. 249
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Preface
Introduction
Prologue: Warming up with Cross Ratios, and the Definition of Moduli Space / 0:
Cross ratios / 0.1:
Definition of moduli space / 0.2:
Stable n-pointed Curves / 1:
n-pointed smooth rational curves / 1.1:
Stable n-pointed rational curves / 1.2:
Stabilization, forgetting marks, contraction / 1.3:
Sketch of the construction of [Characters not reproducible subscript 0,n] / 1.4:
The boundary / 1.5:
Generalizations and references / 1.6:
Stable Maps / 2:
Maps P[superscript 1 Characters not reproducible] P[superscript r] / 2.1:
1-parameter families / 2.2:
Kontsevich stable maps / 2.3:
Idea of the construction of [Characters not reproducible subscript 0,n] (P[superscript r], d) / 2.4:
Evaluation maps / 2.5:
Forgetful maps / 2.6:
Easy properties and examples / 2.7:
Complete conics / 2.9:
Enumerative Geometry via Stable Maps / 2.10:
Classical enumerative geometry / 3.1:
Counting conics and rational cubics via stable maps / 3.2:
Kontsevich's formula / 3.3:
Transversality and enumerative significance / 3.4:
Stable maps versus rational curves / 3.5:
Gromov-Witten Invariants / 3.6:
Definition and enumerative interpretation / 4.1:
Properties of Gromov-Witten invariants / 4.2:
Recursion / 4.3:
The reconstruction theorem / 4.4:
Quantum Cohomology / 4.5:
Quick primer on generating functions / 5.1:
The Gromov-Witten potential and the quantum product / 5.2:
Associativity / 5.3:
Kontsevich's formula via quantum cohomology / 5.4:
Bibliography / 5.5:
Index
Preface
Introduction
Prologue: Warming up with Cross Ratios, and the Definition of Moduli Space / 0:
4.

図書

図書
David J. Green
出版情報: Berlin ; Tokyo : Springer-Verlag, c2003  xi, 138 p. ; 24 cm
シリーズ名: Lecture notes in mathematics ; 1828
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5.

図書

図書
by Jon F. Carlson ... [et al.]
出版情報: Dordrecht : Kluwer Academic, c2003  xv, 776 p. ; 25 cm
シリーズ名: Algebras and applications ; v. 3
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Preface
Acknowledgements
Homological Algebra / 1:
Introduction
Complexes and Sequences / 2:
Projective and Injective Models / 3:
Resolutions / 4:
Ext / 5:
Tensor Products and Tor / 6:
Group Algebras
Duality and Tensor Products
Induction and Restriction
Radicals, Socles and Projective Modules
Degree Shifting
The Stable Category
Group Cohomology and Change of Coefficients / 7:
Projective Resolutions
Minimal Resolutions
The Bar Resolution
Applications to Low Dimensional Cohomology
Restrictions, Inflations and Transfers
Cohomology Products
Yoneda Splices and Compositions of Chain Maps
Products and Group Algebras
Restriction, Inflation and Transfer
Cohomology Ring Computations
Shifted Subgroups and Restrictions
Automorphisms and Cohomology
Spectral Sequences
The Spectral Sequence of a Biocomplex
Products
The Lyndon-Hochschild-Serre Spectral Sequence
Extension Classes
Minimal Resolutions and Convergence
Exact Couples and the Bockstein Spectral Sequence
Norms and the Cohomology of Wreath Products
Wreath Products
The Norm Map
Examples and Applications
Finite Generation of Cohomology
Steenrod Operations
The Steenrod Algebra and Modules
The Steenrod Operations on Cohomology
Cohomology and Modules Over the Steenrod Algebra
The Cohomology of Extraspecial 2-Groups
The Cohomology of Extraspecial p-Groups
Serre's Theorem on the Vanishing of Bocksteins
Varieties and Elementary Abelian Subgroups / 8:
Filtrations on Modules
Vanishing Products of Cohomology Elements
Minimal Primes in Cohomology Rings
The Stratification Theorem
Cohomology Rings of Modules / 9:
Generalized Bocksteins Over Elementary Abelian Groups
Rank Varieties and Cohomology Rings Over Elementary Abelian Groups
The Cohomological Support Variety of a Module
Equating the Rank and Cohomological Support Varieties
The Tensor Product Theorem
Properties of the Cohomological Support Varieties
Complexity and Multiple Complexes / 10:
Notes on Dimension and Rates of Growth
Complexity of Modules
Varieties for Modules with Other Coefficient Rings
Projective Resolutions as Multiple Complexes
Duality Complexes / 11:
Gaps in Cohomology
PoincarF Duality Complexes
Differentials in the HSS
Cohen Macaulay Cohomology Rings
Further Considerations
Transfers, Depth and Detection / 12:
Notes on Depth and Associated Primes
Depth and the p-Rank of the Center
Varieties and Transfers
Detection and Depth-Essential Cohomology
Special Cases
Associated Primes in Cohomology
Unstable Modules
Subgroup Complexes / 13:
Posets of Subgroups and Cell Complexes
Homotopy Equivalences and Equivariance
Complexes of Posets of Finite Groups
The Bouc Complex
Applications to Cohomology
Decompositions of Molecules
Additional Remarks
Cohomology Compositions
Computer Calculations and Completion Tests / 14:
The Visual Cohomology Ring: Generators and Relations
Resolutions, Maps and Homogeneous Parameters
Tests for Completion
Two Special Cases
Appendices: Calculations of the Cohomology Rings of Groups of Order Dividing 64 / J.F. Carlson ; L. Valero-Elizondo ; Mucheng Zhang
Notation and References / A:
Groups of Order 8 / B:
Groups of Order 16 / C:
Groups of Order 32 / D:
Groups of Order 64 / E:
Tables of Krull Dimension and Depth / F:
Tables of Hilbert/PoincarF Series / G:
References
Index
Preface
Acknowledgements
Homological Algebra / 1:
6.

図書

図書
Constantin Bănică and Octavian Stănășilă
出版情報: Bucuresti : Editura Academiei , London ; New York : Wiley, 1976  296 p. ; 25 cm
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7.

図書

図書
Peter Hilton ; course given at the University of São Paulo in the summer of 1968 under the auspices of the Instituto de Pesquisas Matemáticas, Universidade de São Paulo
出版情報: London : Cambridge University Press, 1971  102 p. ; 23 cm
シリーズ名: London Mathematical Society lecture note series ; 1
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General Cohomology Theories / 1:
Exact Couples and Spectral Sequences / 2:
The Generalized Atiyah-Hirzebruch Spectral Sequence / 3:
K- Theory / 4:
K-Theory, the Chern Character and the Hopf Invariant Problem / 5:
General Cohomology Theories / 1:
Exact Couples and Spectral Sequences / 2:
The Generalized Atiyah-Hirzebruch Spectral Sequence / 3:
8.

図書

図書
Yuli B. Rudyak
出版情報: Berlin : Springer, c1998  xii, 587 p. ; 24 cm
シリーズ名: Springer monographs in mathematics
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9.

図書

図書
by P.J. Hilton and S. Wylie
出版情報: Cambridge : University Press, 1960  484 p ; 23 cm
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10.

図書

図書
by Karl H[einrich] Hofmann and Paul S[tallings] Mostert ; with an appendix by Eric C. Nummela
出版情報: Berlin : Deutsche Verl. de Wissenschaften, 1973  236 p. ; 24 cm
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