03346nam 22005895 450 991034931980332120251113210004.09783030272272303027227310.1007/978-3-030-27227-2(CKB)4100000009362562(DE-He213)978-3-030-27227-2(MiAaPQ)EBC5902743(PPN)269146660(EXLCZ)99410000000936256220190923d2019 u| 0engurnn#008mamaatxtrdacontentcrdamediacrrdacarrierHamiltonian Group Actions and Equivariant Cohomology /by Shubham Dwivedi, Jonathan Herman, Lisa C. Jeffrey, Theo van den Hurk1st ed. 2019.Cham :Springer International Publishing :Imprint: Springer,2019.1 online resource (XI, 132 p. 3 illus., 1 illus. in color.)SpringerBriefs in Mathematics,2191-82019783030272265 3030272265 Includes bibliographical references and index.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.SpringerBriefs in Mathematics,2191-8201TopologyGeometryTopologyGeometryTopology.Geometry.Topology.Geometry.514Dwivedi Shubhamauthttp://id.loc.gov/vocabulary/relators/aut1063052Herman Jonathanauthttp://id.loc.gov/vocabulary/relators/autJeffrey Lisa C.1965-authttp://id.loc.gov/vocabulary/relators/autHurk Theo van denauthttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK9910349319803321Hamiltonian Group Actions and Equivariant Cohomology2529863UNINA