Hamiltonian Group Actions and Equivariant Cohomology

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...

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Κύριοι συγγραφείς: Dwivedi, Shubham (Συγγραφέας, http://id.loc.gov/vocabulary/relators/aut), Herman, Jonathan (http://id.loc.gov/vocabulary/relators/aut), Jeffrey, Lisa C. (http://id.loc.gov/vocabulary/relators/aut), van den Hurk, Theo (http://id.loc.gov/vocabulary/relators/aut)
Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
Γλώσσα:English
Έκδοση: Cham : Springer International Publishing : Imprint: Springer, 2019.
Έκδοση:1st ed. 2019.
Σειρά:SpringerBriefs in Mathematics,
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Διαθέσιμο Online:Full Text via HEAL-Link
Περιγραφή
Περίληψη: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.
Φυσική περιγραφή:XI, 132 p. 3 illus., 1 illus. in color. online resource.
ISBN:9783030272272
ISSN:2191-8198
DOI:10.1007/978-3-030-27227-2