{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/86807"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/86807","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Group Actions on Contact Manifolds and Reduction","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.","abstract_html":"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. 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