Mapping class groups are not linear in positive characteristic

2016/10/26 by J. O. Button, Button, J. O.
Mathematics · #FOS: Mathematics #Finite Group Theory Research #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1610.08464

openalex publication_date 2016/10/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For Σ an orientable surface of finite topological type having genus at least 3 (possibly closed or possibly with any number of punctures or boundary components), we show that the mapping class group Mod(Σ) has no faithful linear representation in any dimension over any field of positive characteristic.

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