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.

Keywords

symplectic geometry; symplectic manifolds; Lie groups; momentum maps; Hamiltonian actions; symplectic reduction; Atiyah; Guillemin; Sternberg; convexity theorem; Duistermaat; Heckman; localization theorem

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