Hamiltonian Group Actions and Equivariant Cohomology

• Main Authors: Dwivedi, Shubham (Author, 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)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2019.
• Edition: 1st ed. 2019.
• Series: SpringerBriefs in Mathematics,
• Subjects: Topology.; Geometry.

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...

Table of Contents:

• 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. .