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＜電子ブック＞
Hamiltonian Group Actions and Equivariant Cohomology / by Shubham Dwivedi, Jonathan Herman, Lisa C. Jeffrey, Theo van den Hurk
(SpringerBriefs in Mathematics. ISSN:21918201)

版	1st ed. 2019.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2019
大きさ	XI, 132 p. 3 illus., 1 illus. in color : online resource
著者標目	*Dwivedi, Shubham author Herman, Jonathan author Jeffrey, Lisa C author van den Hurk, Theo author SpringerLink (Online service)
件　名	LCSH:Topology LCSH:Geometry FREE:Topology FREE:Geometry
一般注記	Symplectic vector spaces -- Hamiltonian group actions -- The Darboux-Weinstein Theorem -- Elementary properties of moment maps -- The symplectic structure on coadjoint orbits -- Symplectic Reduction -- Convexity -- Toric Manifolds -- Equivariant Cohomology -- The Duistermaat-Heckman Theorem -- Geometric Quantization -- Flat connections on 2-manifolds. This monograph could be used for a graduate course on symplectic geometry as well as for independent study. The monograph starts with an introduction of symplectic vector spaces, followed by symplectic manifolds and then Hamiltonian group actions and the Darboux theorem. After discussing moment maps and orbits of the coadjoint action, symplectic quotients are studied. The convexity theorem and toric manifolds come next and we give a comprehensive treatment of Equivariant cohomology. The monograph also contains detailed treatment of the Duistermaat-Heckman Theorem, geometric quantization, and flat connections on 2-manifolds. Finally, there is an appendix which provides background material on Lie groups. A course on differential topology is an essential prerequisite for this course. Some of the later material will be more accessible to readers who have had a basic course on algebraic topology. For some of the later chapters, it would be helpful to have some background on representation theory and complex geometry HTTP:URL=https://doi.org/10.1007/978-3-030-27227-2

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