Improved stability ranges in the homology of Torelli and congruence subgroups

2023/09/02 by Bahran, Cihan
#11F75 #18A25 #20J06 (primary) #55U10 (secondary) #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2309.00977

Abstract

We improve the central stability ranges for H2(Torelli subgroup of Aut(Fn)'s) as GL_n(Z)-representations, H2(Torelli subgroup of mapping class groups) as Sp₂g(Z)-representations, Hk(congruence subgroups of GL_n(R)'s) as SL_n^U(R/I)-representations.

Related

• Linear and quadratic ranges in representation stability
• Linear stable range for homology of congruence subgroups via FI-modules
• Modular representations via the first homology of congruence subgroups of mapping class groups and automorphism groups of free groups
• The Stable Homology of Congruence Subgroups
• Towards representation stability for the second homology of the Torelli\n group