2000/08/22 by Eugene Lerman, Lerman, Eugene, Christopher Willett +1 · 1 citation
Mathematics · #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG) #math.SG
paper · pdf · doi:10.48550/arxiv.math/0008178
13 pages
arxiv created 2000/08/22 · openalex publication_date 2000/08/22 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.