Contact Reduction

Details Contact Reduction Contact Reduction

2001-04-06

arxiv.org/abs/math/0104080v4

Mathematics

Symplectic Geometry

14 pages. Presentation and focus significantly improved. Accepted for publication in Trans. AMS

Scientific paper

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 $M_\mu$ at $\mu \in \fg^*$ 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].

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