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Title:Group Actions on Contact Manifolds and Reduction
Author(s):Willett, Christopher Bernard
Doctoral Committee Chair(s):Lerman, Eugene
Department / Program:Mathematics
Discipline:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(s):Mathematics
Abstract:In this thesis I propose a new method for reducing a co-oriented contact manifold M by the action of a Lie group G by contactomorphisms. With a regularity and integrality assumption on mu ∈ g* the contact quotient Mmu, is naturally a co-oriented contact manifold which is independent of the choice of contact form used to represent the given contact structure. Removing the regularity and integrality assumption and replacing it with one concerning the existence of a certain slice for mu ∈ g* , Mmu, is a contact stratified space; i.e., a stratified space equipped with a line bundle which, when restricted to each stratum, defines a co-oriented contact structure. As an application, a direct proof that symplectic quotients are stratified is presented.
Issue Date:2002
Type:Text
Language:English
Description:52 p.
Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2002.
URI:http://hdl.handle.net/2142/86807
Other Identifier(s):(MiAaPQ)AAI3070475
Date Available in IDEALS:2015-09-28
Date Deposited:2002


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