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1.

図書
図書
1. Seminar on micro-local analysis (pbk.)
by Victor W. Guillemin, Masaki Kashiwara, and Takahiro Kawai
出版情報: Princeton, N.J. : Princeton University Press , [Tokyo] : University of Tokyo Press, 1979  vii, 137 p. ; 24 cm
シリーズ名: Annals of mathematics studies ; no. 93
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2.

図書
図書
2. Symplectic techniques in physics
Victor Guillemin, Shlomo Sternberg
出版情報: Cambridge [Cambridgeshire] ; New York : Cambridge University Press, 1984  xi, 468 p. ; 24 cm
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目次情報: 続きを見る
Preface
Introduction / I：
Gaussian optics / 1：
Hamilton's method in Gaussian optics / 2：
Fermat's principle / 3：
From Gaussian optics to linear optics / 4：
Geometrical optics, Hamilton's method, and the theory of geometrical aberrations / 5：
Fermat's principle and Hamilton's principle / 6：
Interference and diffraction / 7：
Gaussian integrals / 8：
Examples in Fresnel optics / 9：
The phase factor / 10：
Fresnel's formula / 11：
Fresnel optics and quantum mechanics / 12：
Holography / 13：
Poisson brackets / 14：
The Heisenberg group and representation / 15：
The Groenwald-van Hove theorem / 16：
Other quantizations / 17：
Polarization of light / 18：
The coadjoint orbit of a semidirect product / 19：
Electromagnetism and the determination of symplectic structures / 20：
Epilogue: Why symplectic geometry?
The geometry of the moment map / II：
Normal forms / 21：
The Darboux-Weinstein theorem / 22：
Kaehler manifolds / 23：
Left-invariant forms and Lie algebra cohomology / 24：
Symplectic group actions / 25：
The moment map and some of its properties / 26：
Group actions and foliations / 27：
Collective motion / 28：
Cotangent bundles and the moment map for semidirect products / 29：
More Euler-Poisson equations / 30：
The choice of a collective Hamiltonian / 31：
Convexity properties of toral group actions / 32：
The lemma of stationary phase / 33：
Geometric quantization / 34：
Motion in a Yang-Mills field and the principle of general covariance / III：
The equations of motion of a classical particle in a Yang-Mills field / 35：
Curvature / 36：
The energy-momentum tensor and the current / 37：
The principle of general covariance / 38：
Isotropic and coisotropic embeddings / 39：
Symplectic induction / 40：
Symplectic slices and moment reconstruction / 41：
An alternative approach to the equations of motion / 42：
The moment map and kinetic theory / 43：
Complete integrability / IV：
Fibrations by tori / 44：
Collective complete integrability / 45：
Collective action variables / 46：
The Kostant-Symes lemma and some of its variants / 47：
Systems of Calogero type / 48：
Solitons and coadjoint structures / 49：
The algebra of formal pseudodifferential operators / 50：
The higher-order calculus of variations in one variable / 51：
Contractions of symplectic homogeneous spaces / V：
The Whitehead lemmas / 52：
The Hochschild-Serre spectral sequence / 53：
Galilean and Poincare elementary particles / 54：
Coppersmith's theory / 55：
References
Index
Preface
Introduction / I：
Gaussian optics / 1：
3.

図書
図書
3. Differential topology
Victor Guillemin, Alan Pollack
出版情報: Englewood Cliffs, N.J. : Prentice-Hall, c1974  xvi, 222 p. ; 24 cm
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4.

図書
図書
4. 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：
5.

図書
図書
5. Symplectic fibrations and multiplicity diagrams
Victor Guillemin, Eugene Lerman, Shlomo Sternberg
出版情報: Cambridge : Cambridge University Press, 1996  xiv, 222 p. ; 24 cm
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6.

図書
図書
6. The spectral theory of Toeplitz operators (: hbk ; : pbk)
by L. Boutet de Monvel and V. Guillemin
出版情報: Princeton, N.J. : Princeton University Press , Tokyo : University of Tokyo Press, 1981  v, 160 p. ; 25 cm
シリーズ名: Annals of mathematics studies ; no. 99
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7.

図書
図書
7. Studies in applied mathematics : a volume dedicated to Irving Segal
edited by Victor Guillemin
出版情報: New York, N.Y. : Academic Press, 1983  xxv, 163 p. ; 24 cm
シリーズ名: Advances in mathematics ; Supplementary studies ; v. 8
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8.

図書
図書
8. Variations on a theme by Kepler
Victor Guillemin and Shlomo Sternberg
出版情報: Providence, R.I. : American Mathematical Society, c1990  vii, 88 p. ; 26 cm
シリーズ名: Colloquium publications / American Mathematical Society ; v. 42
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9.

図書
図書
9. Moment maps and combinatorial invariants of Hamiltonian T[n]-spaces (: us ; : sz)
Victor Guillemin
出版情報: Boston : Birkhäuser, c1994  150 p. ; 25 cm
シリーズ名: Progress in mathematics ; v. 122
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10.

図書
図書
10. Moment maps, cobordisms, and Hamiltonian group actions
Victor Guillemin, Viktor Ginzburg, Yael Karshon
出版情報: Providence, R.I. : American Mathematical Society, c2002  viii, 350 p. ; 26 cm
シリーズ名: Mathematical surveys and monographs ; v. 98
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目次情報: 続きを見る
Introduction
Cobordism: Hamiltonian cobordism Abstract moment maps / Part 1：
The linearization theorem Reduction and applications
Quantization: Geometric quantization / Part 2：
The quantum version of the linearization theorem
Quantization commutes with reduction
Appendices: Signs and normalization conventions / Part 3：
Proper actions of Lie groups
Equivariant cohomology
Stable complex and Spin$^{\mathrm{c}}$structures
Assignments and abstract moment maps
Assignment cohomology Non-degenerate abstract moment maps
Characteristic numbers, non-degenerate cobordisms, and non-virtual quantization
The Kawasaki Riemann-Roch formula Cobordism invariance of the Index of a transversally elliptic operator
Bibliography
Index
Introduction
Cobordism: Hamiltonian cobordism Abstract moment maps / Part 1：
The linearization theorem Reduction and applications
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