Separating subgroups of mapping class groups in homological\n representations

2019/09/03 by Asaf Hadari, Hadari, Asaf
Mathematics · #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

paper · pdf · doi:10.48550/arxiv.1909.01427

openalex publication_date 2019/09/03 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28

Abstract

Let \Γ be either the mapping class group of a closed surface of genus\n\≥ 2, or the automorphism group of a free group of rank \≥ 3. Given any\nhomological representation \ρ of \Γ corresponding to a finite cover,\nand any term \I_k of the Johnson filtration, we show that\n\ρ(\I_k) has finite index in \ρ(\I), the Torelli\nsubgroup of \Γ. Since [\I: \I_k] = \∞ for k >\n1, this implies for instance that no such representation is faithful.\n

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