Open AccessBook
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.
read more
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
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
•Book
4-manifolds and Kirby calculus
Robert E. Gompf,András I. Stipsicz +1 more
- 01 Jan 1999
TL;DR: In this article, the authors introduce surfaces in 4-manifolds complex surfaces and Kirby calculus, a calculus based on handelbodies and Kirby diagrams, which is used for handel bodies and kirby diagrams.
1.8K
•Posted Content
Generalized complex geometry
TL;DR: In this paper, the concept of a generalized Kahler manifold has been introduced, which is equivalent to a bi-Hermitian geometry with torsion first discovered by physicists.
1.4K
Generalized complex geometry
TL;DR: Generalized complex geometry encompasses complex and symplectic ge- ometry as its extremal special cases as mentioned in this paper, including generalized complex branes, which interpolate be- tween at bundles on Lagrangian submanifolds and holomorphic bundles on complex sub-mansifolds, and the basic properties of this geometry, including its enhanced symmetry group, elliptic deforma- tion theory, relation to Poisson geometry, and local structure theory.
Generalized Calabi-Yau manifolds
TL;DR: A geometrical structure on even-dimensional manifolds is defined in this paper, which generalizes the notion of a Calabi-Yau manifold and also a symplectic manifold.
1.2K
Generalized Calabi-Yau manifolds
TL;DR: A geometrical structure on even-dimensional manifolds is defined in this paper, which generalizes the notion of a Calabi-Yau manifold and also a symplectic manifold.
1K
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.
432
Related Papers (5)
Dusa McDuff,Dietmar Salamon +1 more
- 01 Jan 2004
Phillip Griffiths,Joe Harris +1 more
- 01 Jan 1978
Vladimir I. Arnold
- 01 Jan 1974