2016/02/05 by Kathryn Mann, Mann, Kathryn
Mathematics · #Advanced Topology and Set Theory #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematics and Applications #math.GR
paper · pdf · doi:10.48550/arxiv.1602.02146
v2: small additions, typos corrected
openalex publication_date 2016/02/05 · arxiv created 2016/03/09 · arxiv updated 2016/03/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that the group of piecewise linear homeomorphisms of any compact PL manifold does not admit a Polish group topology. This uses a) new results on the relationship between topologies on groups of homeomorphisms, their algebraic structure, and the topology of the underlying manifold, and b) new results on the structure of certain subgroups of PL(M). The proof also shows that the group of piecewise projective homeomorphisms of the circle has no Polish group topology.