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1.

図書
図書
1. Frobenius manifolds, quantum cohomology, and moduli spaces
Yuri I. Manin
出版情報: Providence, R.I. : American Mathematical Society, c1999  xiii, 303 p. ; 27 cm
シリーズ名: Colloquium publications / American Mathematical Society ; v. 47
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2.

図書
図書
2. Supersymmetry and equivariant de Rham theory
Victor W. Guillemin, Shlomo Sternberg
出版情報: Berlin : Springer, 1999  xxiii, 228 p. ; 25 cm
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目次情報: 続きを見る
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：
3.

図書
図書
3. Elliptic cohomology
Charles B. Thomas
出版情報: New York : Kluwer Academic/Plenum, c1999  ix, 199 p. ; 24 cm
シリーズ名: The University series in mathematics
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4.

図書
図書
4. Bivariant periodic cyclic homology (: pbk)
Christian Grønbæk
出版情報: Boca Raton : Chapman & Hall/CRC, c1999  110 p. ; 24 cm
シリーズ名: Research notes in mathematics ; 405
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5.

図書
図書
5. On Thom spectra, orientability, and cobordism
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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6.

図書
図書
6. Cyclic homology. 2nd ed
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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7.

図書
図書
7. Complex algebraic varieties : algebraic curves and their Jacobians (: gw)
A.N. Parshin, I.R. Shafarevich (eds.)
出版情報: Berlin : Springer-Verlag, c1998  270 p. ; 25 cm
シリーズ名: Encyclopaedia of mathematical sciences / editor-in-chief, R.V. Gamkrelidze ; v. 36 . Algebraic geometry ; 3
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目次情報:
Complex Algebraic Varieties
Periods of Integrals and Hodge Structures / Viktor S.Kulikov ; P.V.Kurchanov
Algebraic Curves and Their Jacobians / V.V.Shokurov
Complex Algebraic Varieties
Periods of Integrals and Hodge Structures / Viktor S.Kulikov ; P.V.Kurchanov
Algebraic Curves and Their Jacobians / V.V.Shokurov
8.

図書
図書
8. The book of involutions
Max-Albert Knus ... [et al.] ; with a preface by J. Tits
出版情報: Providence, R.I. : American Mathematical Society, c1998  xxi, 593 p. ; 26 cm
シリーズ名: Colloquium publications / American Mathematical Society ; v. 44
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9.

図書
図書
9. Combinatorial foundation of homology and homotopy : applications to spaces, diagrams, transformation groups, compactifications, differential algebras, algebraic theories, simplicial objects, and resolutions (: [pbk.])
Hans-Joachim Baues
出版情報: Berlin ; Tokyo : Springer, c1999  xv, 362 p. ; 25 cm
シリーズ名: Springer monographs in mathematics
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10.

図書
図書
10. From calculus to cohomology : de Rham cohomology and characteristic classes (: hbk ; : pbk)
Ib Madsen and Jørgen Tornehave
出版情報: Cambridge ; New York : Cambridge University Press, 1997  vii, 286 p. ; 25 cm
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目次情報: 続きを見る
Preface
Introduction / Chapter 1：
The Alternating Algebra / Chapter 2：
de Rham Cohomology / Chapter 3：
Chain Complexes and their Cohomology / Chapter 4：
The Mayer-Vietoris Sequence / Chapter 5：
Homotopy / Chapter 6：
Applications of de Rham Cohomology / Chapter 7：
Smooth Manifolds / Chapter 8：
Differential Forms on Smoth Manifolds / Chapter 9：
Integration on Manifolds / Chapter 10：
Degree, Linking Numbers and Index of Vector Fields / Chapter 11：
The Poincare-Hopf Theorem / Chapter 12：
Poincare Duality / Chapter 13：
The Complex Projective Space CP[superscript n] / Chapter 14：
Fiber Bundles and Vector Bundles / Chapter 15：
Operations on Vector Bundles and their Sections / Chapter 16：
Connections and Curvature / Chapter 17：
Characteristic Classes of Complex Vector Bundles / Chapter 18：
The Euler Class / Chapter 19：
Cohomology of Projective and Grassmannian Bundles / Chapter 20：
Thom Isomorphism and the General Gauss-Bonnet Formula / Chapter 21：
Smooth Partition of Unity / Appendix A：
Invariant Polynomials / Appendix B：
Proof of Lemmas 12.12 and 12.13 / Appendix C：
Exercises / Appendix D：
References
Index
The alternating algebra / 1：
De Rham cohomology / 3：
Chain complexes and their cohomology / 4：
The Mayer-Vietoris sequence / 5：
Applications of De Rham cohomology / 6：
Smooth manifolds / 8：
Differential forms on smooth manifolds / 9：
Integration on manifolds / 10：
Degree, linking numbers and index of vector fields / 11：
The Poincare-Hopf theorem / 12：
Poincare duality / 13：
The complex projective space CPn / 14：
Fiber bundles and vector bundles / 15：
Operations on vector bundles and their sections / 16：
Connections and curvature / 17：
Characteristic classes of complex vector bundles / 18：
The Euler class / 19：
Cohomology of projective and Grassmanian bundles / 20：
Thom isomorphism and the general Gauss-Bonnet formula / 21：
Preface
Introduction / Chapter 1：
The Alternating Algebra / Chapter 2：
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