University of Illinois at Urbana-Champaign
Group Actions on Contact Manifolds and Reduction
Abstract
dc:descriptionIn 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.
Degree
thesis:*- Name thesis:degree_name
- Ph.D.
- Level thesis:degree_level
- Dissertation
- Discipline thesis:degree_discipline
- Mathematics
- Grantor
- University of Illinois at Urbana-Champaign
- Year dc:date
- 2015
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Willett, Christopher Bernard
- Contributors dc:contributor
-
- Lerman, Eugene
Subjects
dc:subject × 1Rights
- Language dc:language
- eng
Identifiers
dc:identifier.*- Identifier
- (MiAaPQ)AAI3070475
- OAI identifier oai:identifier
- oai:www.ideals.illinois.edu:2142/86807