The Topology of Torus Actions on Symplectic Manifolds / by Michèle Audin
(Progress in Mathematics ; 93)
| データ種別 | 電子ブック |
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| 出版情報 | Basel : Birkhäuser Basel , 1991 |
| 本文言語 | 英語 |
| 大きさ | 184 p : online resource |
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| 内容注記 | I Smooth Lie group actions on manifolds 1 Generalities 2 Equivariant tubular neighborhoods and orbit types decomposition 3 Examples: 2 and 3-dimensional S1-manifolds II Symplectic geometry 1 Symplectic manifolds 2 Hamiltonian vector fields and Poisson manifolds 3 Symplectic and hamiltonian actions III Morse theory for hamiltonians 1 Critical points of almost periodic hamiltonians 2 Morse functions (in the sense of Bott) 3 Connectivity of the fibers of the moment map 4 Application to convexity theorems IV About manifolds of this dimension 1 Characterisation of those circle actions which are hamiltonian 2 Symplectic reduction of the regular levels for a periodic hamiltonian 3 Blowing up fixed points; creation of index 2 critical points 4 4-manifolds with periodic hamiltonians 5 Plumbing A Appendix: compact symplectic SU(2)-manifolds of dimension 4 B Appendix: 4-dimensional S1-manifolds with no invariant symplectic form (examples) V Equivariant cohomology and the Duistermaat-Heckman theorems 1 Principal and universal bundles 2 The Borel construction and equivariant cohomology 3 Equivariant cohomology and hamiltonian actions 4 Duistermmat-Heckman with singularities 5 Localisation at fixed points 6 The Duistermaat-Heckman formula A Appendix: some algebraic topology B Appendix: various notions of Euler classes VI Toric manifolds 1 The action of TNC and its subgroups on CN 2 Fans and toric varieties 3 Fans, symplectic reduction, convex polyhedra 4 Properties of the toric manifolds X? 5 Complex toric surfaces References |
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| 著者標目 | *Audin, Michèle author SpringerLink (Online service) |
| 件 名 | LCSH:Mathematics LCSH:Algebraic geometry FREE:Mathematics FREE:Algebraic Geometry |
| 分 類 | DC23:516.35 |
| 巻冊次 | ISBN:9783034872218 
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| ISBN | 9783034872218 |
| URL | http://dx.doi.org/10.1007/978-3-0348-7221-8 |
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