Quantitative representation stability over linear groups

Jeremy Miller, Jennifer C. H. Wilson

Published 2017-09-12Version 1

We introduce a technique for proving quantitative representation stability theorems for sequences of representations of certain finite linear groups. We apply these techniques to the rational homology of congruence subgroups of mapping class groups and congruence subgroups of automorphism groups of free groups. This partially resolves a question raised by Church and Putman--Sam. We also prove new homological stability results for mapping class groups and automorphism groups of free groups with twisted coefficients.