Johnsonʹs homomorphisms of subgroups of the mapping class group, the Magnus expansion and Massey higher products of mapping tori

Johnsonʹs homomorphism τk of the subgroup of the mapping class group of surfaces is defined via the action on the lower central series of the fundamental group. We give some descriptions of τk by using the Magnus expansion and thereby give a geometric meaning to it in terms of the Massey products on mapping tori of the corresponding mapping classes.