Hamiltonian Torus Actions on Symplectic Manifolds
Publication date
Authors
DOI
Document Type
Bachelor Thesis
Metadata
Show full item recordCollections
License
CC-BY-NC-ND
Abstract
This thesis is concerned with the study of Hamiltonian torus actions on symplectic manifolds. A Hamiltonian T-space consists of a symplectic manifold equipped with an action of a torus together with a momentum map. To study this object, we discuss symplectic reduction, the Atiyah--Guillemin--Sternberg convexity theorem and the Duistermaat--Heckman theorems.
Keywords
symplectic geometry; symplectic manifolds; Lie groups; momentum maps; Hamiltonian actions; symplectic reduction; Atiyah; Guillemin; Sternberg; convexity theorem; Duistermaat; Heckman; localization theorem