On the Hamiltonian circle actions and symplectic reduction

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Thesis Type: Postgraduate

Institution Of The Thesis: Orta Doğu Teknik Üniversitesi, Faculty of Arts and Sciences, Department of Mathematics, Turkey

Approval Date: 2003

Student: ALİ SAİT DEMİR

Supervisor: YILDIRAY OZAN

Abstract:

Given a symplectic manifold, it is of interest how Lie group actions, their orbit spaces look like and what are some topological requirements on the existence of such actions. In this thesis we present the work of Ono, giving some sufficient conditions for non-existence of circle actions on symplectic manifolds and work of Li, describing the fundamental groups of symplectic reductions of circle actions.