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The Topological Structure of Contact and Symplectic Quotients

Eugene Lerman·Christopher Willett
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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.

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Eugene Lerman, Christopher Willett. 2000-08-22. The Topological Structure of Contact and Symplectic Quotients. https://arxiv.org/abs/math/0008178

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