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作者 Dwivedi, Shubham, author
書名 Hamiltonian group actions and equivariant cohomology / by Shubham Dwivedi, Jonathan Herman, Lisa C. Jeffrey, Theo van den Hurk
出版項 Cham : Springer International Publishing : Imprint: Springer, 2019
國際標準書號 9783030272272 (electronic bk.)
9783030272265 (paper)
國際標準號碼 10.1007/978-3-030-27227-2 doi
book jacket
說明 1 online resource (xi, 132 pages) : illustrations, digital ; 24 cm
text txt rdacontent
computer c rdamedia
online resource cr rdacarrier
text file PDF rda
系列 SpringerBriefs in mathematics, 2191-8198
SpringerBriefs in mathematics
附註 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
Host Item Springer eBooks
主題 Symplectic geometry
Homology theory
Topology
Geometry
Alt Author Herman, Jonathan, author
Jeffrey, Lisa C., author
van den Hurk, Theo, author
SpringerLink (Online service)
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