Separating subgroups of mapping class groups in homological representations

Abstract

Let [Formula: see text] be either the mapping class group of a closed surface of genus [Formula: see text], or the automorphism group of a free group of rank [Formula: see text]. Given any homological representation [Formula: see text] of [Formula: see text] corresponding to a finite cover, and any term [Formula: see text] of the Johnson filtration, we show that [Formula: see text] has finite index in [Formula: see text], the Torelli subgroup of [Formula: see text]. Since [Formula: see text] for [Formula: see text], this implies for instance that no such representation is faithful.