Audin The Topology of Torus Actions on Symplectic Manifolds

1991
ISBN: 978-3-0348-7221-8
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 93, 184 Seiten, eBook

Reihe: Progress in Mathematics

Zielgruppe

Research

Autoren/Hrsg.

Audin, Michèle

Inhaltsverzeichnis

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.