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1.

図書

図書
Nikolai Saveliev
出版情報: Berlin ; Tokyo : Springer, c2002  xii, 223 p. ; 24 cm
シリーズ名: Encyclopaedia of mathematical sciences / editor-in-chief, R.V. Gamkrelidze ; v. 140 . Low-dimensional topology / R.V. Gamkrelidze, V.A. Vassiliev (eds.) ; 1
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目次情報: 続きを見る
Homology 3-Spheres / 1:
Integral Homology 3 Spheres / 1.1:
Homotopy 3-Spheres / 1.1.1:
Poincaré Homology Sphere / 1.1.2:
Brieskorn Homology Spheres / 1.1.3:
Seifert Fibered Homology Spheres / 1.1.4:
Dehn Surgery on Knots / 1.1.5:
Surgery on Links / 1.1.6:
Connected Sums and Splicing / 1.1.7:
Splice Decomposition / 1.1.8:
Plumbing / 1.1.9:
Links of Singularities / 1.1.10:
Mutations / 1.1.11:
Branched Covers / 1.1.12:
Heegaard Splittings of Homology Spheres / 1.1.13:
Rational Homology Spheres / 1.2:
Spherical Space Forms / 1.2.1:
Dehn Surgery / 1.2.2:
Seifert Fibered Manifolds / 1.2.3:
Rokhlin Invariant / 1.2.4:
The Rokhlin Theorem / 2.1:
Definition of the Rokhlin Invariant / 2.2:
Properties of the Rokhlin Invariant / 2.3:
Surgery Formula for the Rokhlin Invariant / 2.3.1:
Surgery on Algebraically Split Links / 2.3.2:
Splicing and Mutation / 2.3.3:
Rokhlin Invariant of Branched Coverings / 2.3.4:
Birman-Craggs Homomorphisms / 2.3.5:
Homology Cobordism Invariance / 2.3.6:
Seifert Fibered and Graph Homology Spheres / 2.4:
The Algorithm / 2.4.1:
The Formula / 2.4.2:
Casson Invariant / 3:
Definition of the Casson Invariant / 3.1:
Construction of the Casson Invariant / 3.2:
SU(2)-Represcntation Spaces / 3.2.1:
The Intersection Theory / 3.2.2:
Orientations / 3.2.3:
Independence of Heegaard Splitting / 3.2.4:
Casson Invariant for Knots and Property (1) / 3.2.5:
The Difference Cycle / 3.2.6:
Casson Invariant for Boundary Links and Property (2) / 3.2.7:
Casson Invariant of a Trefoil and Property (0) / 3.2.8:
Comments and Ramifications / 3.3:
Pillowcase / 3.3.1:
Perturbations / 3.3.2:
The Connected Sum Formula / 3.3.3:
The Integrality of λ(Σ) / 3.3.4:
Casson Invariant of Algebraically Split Links / 3.3.5:
Properties of the Casson Invariant / 3.4:
Splicing Additivity / 3.4.1:
Mutation Invariance / 3.4.2:
Casson Invariant of Branched Coverings / 3.4.3:
Casson Invariant of Fibered Knots / 3.4.4:
Finite Type Invariants / 3.4.5:
Further Properties of the Casson Invariant / 3.4.6:
Casson Invariant of Σ(p, q, r) / 3.5:
Casson Invariant of Σ(a1, …, an) / 3.5.2:
The Neumann-Wahl Conjecture / 3.5.3:
Applications of the Casson Invariant / 3.6:
Triangulating Topological 4-Manifolds / 3.6.1:
Arnphicheiral Homology Spheres / 3.6.2:
Property P for Knots / 3.6.3:
Invariants of Walker and Lescop / 4:
Definition of the Walker Invariant / 4.1:
Construction of the Walker Invariant / 4.2:
SU(2)-Representation Varieties / 4.2.1:
The Surgery Formula / 4.2.2:
Combinatorial Definition of the Walker Invariant / 4.2.4:
The Lescop Invariant / 4.3:
Properties of the Walker and Lescop Invariants / 4.4:
The Gluing Formula / 4.4.1:
Casson Type Invariants from Other Lie Groups / 4.4.2:
Casson Invariant and Gauge Theory / 5:
Gauge Theory in Dimension 3 / 5.1:
Chern-Simons Function / 5.2:
The Casson Invariant from Gauge Theory / 5.3:
Morse Theory and Euler Characteristic / 5.3.1:
Critical Points of cs and Spectral Flow / 5.3.2:
Non-degenerate Case / 5.3.3:
Morse type Perturbations / 5.3.4:
Casson Invariant and Seiberg-Witten Equations / 5.3.6:
Casson-type Invariants of Knots / 5.4:
Representation Varieties of Knot Groups / 5.4.1:
The Invariants / 5.4.2:
Equivariant Casson Invariant / 5.5:
Equivariant Gauge Theory / 5.5.1:
Definition of the Invariants / 5.5.2:
Equivariant Casson and Knot Signatures / 5.5.3:
Applications / 5.5.4:
The SU(3) Casson Invariant / 5.6:
Some SU(3)-Gauge Theory / 5.6.1:
Definition of the Invariant / 5.6.2:
Properties and Computations / 5.6.3:
Instanton Floer Homology / 6:
Gauge Theory in Dimension 4 / 6.1:
Gauge Theory on Closed 4-Manifolds / 6.1.1:
Gauge Theory on Open 4-Manifolds / 6.1.2:
Linear Analysis / 6.1.3:
Non-linear Analysis / 6.1.4:
Definition of the Floer Homology / 6.2:
Review of the Morse Theory / 6.2.1:
Floer Homology of Integral Homology Spheres / 6.2.2:
Functoriality with Respect to Cobordisms / 6.2.3:
Spectral Flow Formulas / 6.3:
The Atiyah-Patodi-Singer Formula / 6.3.1:
The Splitting Formula / 6.3.2:
The Kirk-Klassen Formula / 6.3.3:
The Closed Form Formula / 6.4:
Graph Homology Spheres / 6.4.3:
Properties of the Floer Homology / 6.5:
Orientation Reversal / 6.5.1:
Floer Homology of Homology Handles / 6.5.2:
The Floer Exact Triangle / 6.5.3:
Special Boundary Maps / 6.5.4:
The u-map in Floer Homology / 6.5.5:
Integer Graded Floer Homology / 6.5.6:
Floer Homology of Connected Sums / 6.5.7:
Functoriality with Respect to Diffeornorphisms / 6.5.8:
Floer Homology in Donaldson Theory / 6.5.9:
Donaldson Invariants of Closed 4-Manifolds / 6.6.1:
Relative Donaldson Polynomials / 6.6.2:
Extending Floer Homology / 6.6.3:
Equivariant Floer Homology / 6.7.1:
Fukaya-Floer Homology / 6.7.2:
Floer's Category and Functor / 6.7.3:
The Atiyah-Floer Conjecture / 6.7.4:
Floer Homology of Knots / 6.7.5:
Seiberg-Witten Floer Homology / 6.7.6:
The Homology Cobordism Group / 7:
Homology Cobordisms / 7.1:
Mazur Homology Spheres / 7.1.1:
Knot Cobordisms and Homology Cobordisms / 7.1.2:
Ribbon Concordances and Ribbon Knots / 7.1.3:
Branched Coverings / 7.1.4:
The Structure of <$>\Theta_{\op Z}^3<$> / 7.2:
A Classical Approach to <$>\Theta_{\op Z}^3<$> / 7.2.1:
Infinite Order Elements in <$>\Theta_{\op Z}^3<$> / 7.2.2:
The <$>\bar \mu<$>-Invariant / 7.2.3:
The Fukumoto-Furuta Invariants / 7.2.4:
The Group <$>\Theta_{\op Z}^3<$> is Infinitely Generated / 7.2.5:
Applications of the Homology Cobordism Group / 7.3:
Triangulating Topological Manifolds / 7.3.1:
Knot Concordance Group / 7.3.2:
PL-discs in Contractible 4-Manifolds / 7.3.3:
Constructing Smooth Manifolds / 7.3.4:
References
Index
Homology 3-Spheres / 1:
Integral Homology 3 Spheres / 1.1:
Homotopy 3-Spheres / 1.1.1:
2.

図書

図書
V.A. Vassiliev
出版情報: Providence, R.I. : American Mathematical Society, c2002  xi, 324 p. ; 26 cm
シリーズ名: Mathematical surveys and monographs ; v. 97
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3.

図書

図書
V.A. Vassiliev ; translated by A. Sossinski
出版情報: Providence, R.I. : American Mathematical Society, c2001  xiii, 149 p. ; 22 cm
シリーズ名: Student mathematical library ; v. 14
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目次情報: 続きを見る
Topological spaces and operations with them
Homotopy groups and homotopy equivalence
Coverings Cell spaces ($CW$-complexes)
Relative homotopy groups and the exact sequence of a pair
Fiber bundles
Smooth manifolds
The degree of a map
Homology: Basic definitions and examples
Main properties of singular homology groups and their computation
Homology of cell spaces
Morse theory
Cohomology and Poincare duality
Some applications of homology theory
Multiplication in cohomology (and homology)
Index of notations Subject
Index
Topological spaces and operations with them
Homotopy groups and homotopy equivalence
Coverings Cell spaces ($CW$-complexes)
4.

図書

図書
B. Feigin, V. Vassiliev, editors
出版情報: Providence, R.I. : American Mathematical Society, c1998  xiv, 182 p. ; 26 cm
シリーズ名: American Mathematical Society translations ; ser. 2, v. 185 . Advances in the mathematical sciences (formerly advances in Soviet mathematics) ; 38
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5.

図書

図書
A. Khovanskiĭ, A. Varchenko, V. Vassiliev, editors ; [translation edited by A.B. Sossinsky]
出版情報: Providence, R.I. : American Mathematical Society, c1997  xiii, 255 p. ; 26 cm
シリーズ名: American Mathematical Society translations ; ser. 2, v. 180 . Advances in the mathematical sciences (formerly Advances in Soviet Mathematics) ; 34
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6.

図書

図書
by V.A. Vassiliev
出版情報: Dordrecht ; Boston : Kluwer Academic Publishers, c1995  xvii, 289 p. ; 25 cm
シリーズ名: Mathematics and its applications ; v. 315
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目次情報: 続きを見る
Introduction
Picard-Lefschetz-Pham theory and singularity theory / I:
Newton's theorem on the nonintegrability of ovals / II:
Newton's potential of algebraic layers / III:
Lacunas and the local Petrovskii condition for hyperbolic differential operators with constant coefficients / IV:
Calculation of local Petrovskii cycles and enumeration of local lacunas close to real function singularities / V:
a FORTRAN program searching for the lacunas and enumerating the morsifications of real function singularities / Appendix:
Bibliography
Index
Introduction
Picard-Lefschetz-Pham theory and singularity theory / I:
Newton's theorem on the nonintegrability of ovals / II:
7.

図書

図書
V.A. Vassiliev
出版情報: Providence, R.I. : American Mathematical Society, c1992  vi, 208 p. ; 27 cm
シリーズ名: Translations of mathematical monographs ; v. 98
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目次情報: 続きを見る
Sum formulas and Ext-groups / H. H. Andersen
Schur-Weyl duality in positive characteristic / S. Doty
The centers of Iwahori-Hecke algebras are filtered / A. Francis ; W. Wang
University of Georgia Vigre Algebra Group, On Kostant's theorem for Lie algebra cohomology $G$-stable pieces and partial flag varieties / X. He
Steinberg representations and duality properties of arithmetic groups, mapping class groups, and outer automorphism groups of free groups / L. Ji
Characters of simplylaced nonconnected groups versus characters of nonsimplylaced connected groups / S. Kumar ; G. Lusztig ; D. Prasad
Classification of finite-dimensional basic Hopf algebras according to their representation type / G. Liu
Twelve bridges from a reductive group to its Langlands dual
Some new highest weight categories / B. J. Parshall ; L. L. Scott
Classification of quasi-trigonometric solutions of the classical Yang-Baxter equation / I. Pop ; A. Stolin
The relevance and the ubiquity of Prufer modules / C. M. Ringel
Quivers and the Euclidean group / A. Savage
$\mathfrak {eu}_2$-Lie admissible algebras and Steinberg unitary Lie algebras / S. Shang ; Y. Gao
Lusztig's conjecture for finite classical groups with even characteristic / T. Shoji
A survey on quasifinite representations of Weyl type Lie algebras / Y. Su
Maximal and primitive elements in baby Verma modules for type $B_2$ / N. Xi
Irreducible representations of the special algebras in prime characteristic / Y.-F. Yao ; B. Shu
Sum formulas and Ext-groups / H. H. Andersen
Schur-Weyl duality in positive characteristic / S. Doty
The centers of Iwahori-Hecke algebras are filtered / A. Francis ; W. Wang
8.

図書

図書
Peter Kuchment, Vladimir Lin, editors
出版情報: Providence, R.I. : American Mathematical Society, c1998  xxvi, 263 p. ; 26 cm
シリーズ名: American Mathematical Society translations ; ser. 2, v. 184 . Advances in the mathematical sciences (formerly advances in Soviet mathematics) ; 37
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9.

図書

図書
A. Khovanskiĭ, A. Varchenko, V. Vassiliev, editors
出版情報: Providence, R.I. : American Mathematical Society, c1998  xi, 194 p. ; 26 cm
シリーズ名: American Mathematical Society translations ; ser. 2, v. 186 . Advances in the mathematical sciences (formerly advances in Soviet mathematics) ; 39
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目次情報: 続きを見る
Lagrangian reduction, the Euler-Poincare equations, and semidirect products / H. Cendra ; D. D. Holm ; J. E. Marsden ; T. S. Ratiu
Lagrangian intersection theory: Finite-dimensional approach / Y. Eliashberg ; M. Gromov
Multiplicity of a Noetherian intersection / A. Gabrielov ; A. Khovanskii
Sixth Painleve equation, universal elliptic curve, and mirror of ${\mathbf P}^2$ / Yu. I. Manin
Convex hulls of random processes / Ya. G. Sinai
Mutual position of hypersurfaces in projective space / O. Viro
Hochschild cohomology and characteristic classes for star-products / A. Weinstein ; P. Xu
Lagrangian reduction, the Euler-Poincare equations, and semidirect products / H. Cendra ; D. D. Holm ; J. E. Marsden ; T. S. Ratiu
Lagrangian intersection theory: Finite-dimensional approach / Y. Eliashberg ; M. Gromov
Multiplicity of a Noetherian intersection / A. Gabrielov ; A. Khovanskii
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