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Introduction to symplectic topology
Dusa McDuff,Dietmar Salamon +1 more
- 01 Jan 1995
TL;DR: In this article, the authors present a survey of the history of classical and modern manifold geometry, from classical to modern, including linear and almost complex structures, and the Arnold conjecture of the group of symplectomorphisms.
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Abstract: Introduction I. FOUNDATIONS 1. From classical to modern 2. Linear symplectic geometry 3. Symplectic manifolds 4. Almost complex structures II. SYMPLECTIC MANIFOLDS 5. Symplectic group actions 6. Symplectic fibrations 7. Constructing symplectic manifolds III. SYMPLECTOMORPHISMS 8. Area-preserving diffeomorphisms 9. Generating functions 10. The group of symplectomorphisms IV. SYMPLECTIC INVARIANTS 11. The Arnold conjecture 12. Symplectic capacities 13. New directions
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Citations
Finsler interpolation inequalities
TL;DR: In this article, the equivalence between Sturm, Lott and Villani's curvature-dimension condition and a lower Ricci curvature bound for Finsler manifolds was established.
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Algebraic models in geometry
Ives Felix,John Oprea,Daniel Tanré +2 more
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TL;DR: A Florilege of Geometric Applications as mentioned in this paper is a collection of geometrical applications in which Lie Groups and Homogeneous Spaces have been used for a wide range of purposes, e.g.
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An Invitation to Morse Theory
Liviu I. Nicolaescu
- 28 Mar 2007
TL;DR: The topology of Morse Functions and its application in Morse-Smale Flows and Whitney Stratifications can be found in this article, where Morse Functions can be expressed as Morse Functions.
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Singular reduction and quantization
Eckhard Meinrenken,Reyer Sjamaar +1 more
TL;DR: In this article, it was shown that the equivariant index of a compact prequantizable manifold M is invariant to the Riemann-Roch number of the singular quotient of the manifold, provided the quotient is nonsingular.
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A link invariant from the symplectic geometry of nilpotent slices
Paul Seidel,Ivan Smith +1 more
TL;DR: In this article, the authors define an invariant of oriented links in S 3 using the symplectic geometry of certain spaces which arise naturally in Lie theory and present a knot as the closure of a braid, which in turn views as a loop in configuration space.
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References
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Heat Kernels and Dirac Operators
Nicole Berline,Ezra Getzler,Michèle Vergne +2 more
- 01 Apr 1992
TL;DR: In this article, the authors present a formal solution for the trace of the heat kernel on Euclidean space, and show that the trace can be used to construct a heat kernel of an equivariant vector bundle.
2.5K
The topology of torus actions on symplectic manifolds
Michèle Audin
- 01 Jan 1991
TL;DR: The Topology of Torus Actions on Symplectic Manifolds as mentioned in this paper is an extended version of the first edition of the Torus Action on Symmlectic manifolds published in 1991.
432
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