The topological structure of contact and symplectic quotients (Q2708374)

The authors prove two main results. The first one shows (without freeness assumption) that, in general, contact quotients are naturally stratified spaces. It can be shown that the strata of a contact quotient are contact manifolds. The second one is a natural short proof that symplectic quotients are stratified spaces. The proof uses the fact that neighborhoods of singularities of symplectic quotients are products of a disk with a cone on a contact reduced space. They prove the two main theorems simultaneously. The proof has two ingredients: the first one is the observation that arbitrary contact quotients are modeled on the contact quotients of contact vector spaces and that arbitrary symplectic quotients are modeled on the symplectic quotients of symplectic vector spaces. The second one is in Lemma 3.3 wich describes the structure of contact and symplectic quotients of vector spaces. They give a short proof of the fact that connected contact and symplectic quotients have unique connected open dense strata. In the paper one can also see a short review of some results of group actions on co-oriented contact manifolds.