2011/10/17 by Thomas Koberda, Koberda, Thomas
Mathematics · #57M10 (Primary) 57M27 (Secondary) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #math.GR #math.GT #msc:57M10 #msc:57M27
paper · pdf · doi:10.48550/arxiv.1110.3743
18 pages
arxiv created 2011/10/17 · openalex publication_date 2011/10/17 · arxiv updated 2011/10/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let Σ be a surface whose interior admits a hyperbolic structure of finite volume. In this paper, we show that any infinite order mapping class acts with infinite order on the homology of some universal k--step nilpotent cover of Σ. We show that a Torelli mapping class either acts with infinite order on the homology of a finite abelian cover, or the suspension of the mapping class is a 3--manifold whose fundamental group has positive homology gradient. In the latter case, it follows that the suspended 3--manifold has a large fundamental group. It follows that every element of the Magnus kernel suspends to give a 3--manifold with a large fundamental group.