2001/04/06 by Christopher Willett, Willett, Christopher · 1 citation
Engineering · Mathematics · #53D10 #53D20 #Advanced Numerical Analysis Techniques #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Symplectic Geometry (math.SG) #math.DG #math.DS #math.SG #msc:53D10 #msc:53D20
paper · pdf · doi:10.48550/arxiv.math/0104080
14 pages. Presentation and focus significantly improved. Accepted for publication in Trans. AMS
openalex publication_date 2001/04/06 · arxiv created 2002/03/14 · arxiv updated 2009/11/30 · openalex created_date 2024/04/10 · openalex updated_date 2026/07/28
In this article I propose a new method for reducing a co-oriented contact manifold M equipped with an action of a Lie group G by contact transformations. With a certain regularity and integrality assumption the contact quotient Mμ at μ∈ \fg^* is a naturally a co-oriented contact orbifold which is independent of the contact form used to represent the given contact structure. Removing the regularity and integrality assumptions and replacing them with one concerning the existence of a slice, which is satisfied for compact symmetry groups, results in 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. This extends the previous work of the author and E. Lerman [LW].