Contact reduction

Christopher Willett
2002 Transactions of the American Mathematical Society  
In this article I propose a new method for reducing 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 ∈ g * is a naturally 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
more » ... 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.
doi:10.1090/s0002-9947-02-03045-3 fatcat:5xxy4ea2gfgh3gmm2cm2sfecuy