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Lerman, Eugene Willett, Christopher Bernard 2015-09-28T15:19:38Z 2015-09-28T15:19:38Z 10000-01-01 2002 2002 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. Made available in DSpace on 2015-09-28T15:19:38Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 3070475.pdf: 2288321 bytes, checksum: f4f72050fbf8df75074a6f3a535e6d4f (MD5) Previous issue date: 2002 Embargo set by: Seth Robbins for item 88088 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs U of I Only 52 p. Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2002. http://hdl.handle.net/2142/86807 (MiAaPQ)AAI3070475 eng Mathematics Group Actions on Contact Manifolds and Reduction text Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.