Homeomorphism groups of 2-manifolds with the virtual Rokhlin property

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.

v3: Incorporated referee's comments, the article has been accepted for publication by the Journal of Topology. v2: Updated discussion in the introduction under geometric consequences; 25 pages, 3 figures