Every Infinite order mapping class has an infinite order action on the homology of some finite cover

2015/08/06 by Asaf Hadari, Hadari, Asaf
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #math.GT

paper · pdf · doi:10.48550/arxiv.1508.01555

arxiv created 2015/08/06 · arxiv updated 2015/08/10

Abstract

We prove the following well known conjecture: let Σ be an oriented surface of finite type whose fundamental group is a nonabelian free group. Let ϕ∈ \textupMod(Σ) be a an infinite order mapping class. Then there exists a finite solvable cover \widehatΣ → Σ, and a lift \widehatϕ of ϕ such that the action of \widehatϕ on H₁(\widehatΣ, ℤ) has infinite order. Our main tools are the theory of homological shadows, which was previously developed by the author, and Fourier analysis

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