Hamiltonian Torus Actions on Symplectic Manifolds

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.