LEADER 03346nam 22005895 450 001 9910349319803321 005 20251113210004.0 010 $a9783030272272 010 $a3030272273 024 7 $a10.1007/978-3-030-27227-2 035 $a(CKB)4100000009362562 035 $a(DE-He213)978-3-030-27227-2 035 $a(MiAaPQ)EBC5902743 035 $a(PPN)269146660 035 $a(EXLCZ)994100000009362562 100 $a20190923d2019 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aHamiltonian Group Actions and Equivariant Cohomology /$fby Shubham Dwivedi, Jonathan Herman, Lisa C. Jeffrey, Theo van den Hurk 205 $a1st ed. 2019. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2019. 215 $a1 online resource (XI, 132 p. 3 illus., 1 illus. in color.) 225 1 $aSpringerBriefs in Mathematics,$x2191-8201 311 08$a9783030272265 311 08$a3030272265 320 $aIncludes bibliographical references and index. 327 $aSymplectic 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. . 330 $aThis monograph could be used for a graduate course on symplectic geometry as well as for independent study. The monograph starts with an introduction of symplectic vector spaces, followed by symplectic manifolds and then Hamiltonian group actions and the Darboux theorem. After discussing moment maps and orbits of the coadjoint action, symplectic quotients are studied. The convexity theorem and toric manifolds come next and we give a comprehensive treatment of Equivariant cohomology. The monograph also contains detailed treatment of the Duistermaat-Heckman Theorem, geometric quantization, and flat connections on 2-manifolds. Finally, there is an appendix which provides background material on Lie groups. A course on differential topology is an essential prerequisite for this course. Some of the later material will be more accessible to readers who have had a basic course on algebraic topology. For some of the later chapters, it would be helpful to have some background on representation theory and complex geometry. 410 0$aSpringerBriefs in Mathematics,$x2191-8201 606 $aTopology 606 $aGeometry 606 $aTopology 606 $aGeometry 615 0$aTopology. 615 0$aGeometry. 615 14$aTopology. 615 24$aGeometry. 676 $a514 700 $aDwivedi$b Shubham$4aut$4http://id.loc.gov/vocabulary/relators/aut$01063052 702 $aHerman$b Jonathan$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aJeffrey$b Lisa C.$f1965-$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aHurk$b Theo van den$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910349319803321 996 $aHamiltonian Group Actions and Equivariant Cohomology$92529863 997 $aUNINA