Arithmetic representations of mapping class groups

2021/08/29 by Looijenga, Eduard
#11E39 #57K20 #57M12 #Algebraic Geometry (math.AG) #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2108.12791

Abstract

Let S be a closed oriented surface and G a finite group of orientation preserving automorphisms of S whose orbit space has genus at least 2. There is a natural group homomorphism from the G-centralizer in Diff⁺(S) to the G-centralizer in Sp(H₁(S)). We give a sufficient condition for its image to be a subgroup of finite index and a weaker condition for this to have no finite nonzero orbit (the Putman-Wieland property).

Related

• Homological representations of low genus mapping class groups
• Representations of surface groups with finite mapping class group orbits
• Canonical representations of surface groups
• Representations of surface groups with universally finite mapping class group orbit
• Representations of the mapping class group of a non-orientable surface