Homeomorphism groups of 2-manifolds with the virtual Rokhlin property

2023/08/25 by Justin Lanier, Lanier, Justin, Nicholas G. Vlamis +1
Mathematics · #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Advanced Topology and Set Theory

paper · pdf · doi:10.48550/arxiv.2308.13138

Abstract

We introduce and motivate the definition of the virtual Rokhlin property for topological groups. We then classify the 2-manifolds whose homeomorphism groups have the virtual Rokhlin property. We also establish the analogous result for mapping class groups of 2-manifolds.

Related

• Homeomorphism groups of self-similar 2-manifolds
• Homeomorphism groups of telescoping 2-manifolds are strongly distorted
• Uniform first order interpretation of the second order theory of countable groups of homeomorphisms
• Twisted Rokhlin property for mapping class groups
• Virtual pro-p properties of 3-manifold groups