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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
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The bounded isometry conjecture for the Kodaira-Thurston manifold and 4-Torus
TL;DR: In this article, it was shown that the bounded isometry conjecture holds for the Kodaira-Thurston manifold with the standard symplectic form and for the 4-torus with all linear symplectic forms.
5
Tight Beltrami fields with symmetry
TL;DR: In this article, a suitable adapted Riemannian metric for the volume and curvature of a Seifered fibered 3-manifold without a boundary was proposed, which implies universal tightness of the contact structure.
5
•Posted Content
Virtual Morse theory on $\Omega Ham(M,\omega)$
TL;DR: In this paper, it was shown that the Hofer length functional behaves "virtually" as a perfect Morse-Bott functional with a flow, which can be applied to study topology and Hofer geometry.
5
Semisimple coadjoint orbits and cotangent bundles
TL;DR: In this paper, a connection between the Iwasawa horospherical projection and the symplectic geometry of real hyperbolic (co)adjoint orbits is established, based on elementary results on both Lie theory and cosine geometry.
5
Hamiltonian unknottedness of certain monotone Lagrangian tori in $S^2\times S^2$
TL;DR: In this paper, it was shown that a monotone Lagrangian torus in $S 2 times S 2$ which suitably sits in a symplectic fibration with two sections in its complement is Hamiltonian isotopic to the Clifford torus.
5
References
•Book
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.
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