The Topological Structure of Contact and Symplectic Quotients

TL;DR

This paper demonstrates that contact and symplectic quotients resulting from proper group actions are topologically stratified spaces, providing a unified and simplified understanding of their structure in contact and symplectic geometry.

Contribution

It establishes that contact quotients are topologically stratified spaces and extends this result to symplectic quotients, simplifying previous complex proofs.

Findings

Contact quotients are topologically stratified spaces.

Symplectic quotients for proper Hamiltonian actions are topologically stratified.

Provides a unified framework for understanding quotients in contact and symplectic geometry.

Abstract

We show that if a Lie group acts properly on a co-oriented contact manifold preserving the contact structure, then the contact quotient is topologically a stratified space (in the sense that a neighborhood of a point in the quotient is a product of a disk with a cone on a compact stratified space). As a corollary, we obtain that symplectic quotients for proper Hamiltonian actions are topologically stratified spaces in this strong sense thereby extending and simplifying previous work.