The top homology group of the genus 3 Torelli group

Abstract

AbstractThe Torelli group of a genus oriented surface is the subgroup of the mapping class group consisting of all mapping classes that act trivially on . The quotient group is isomorphic to the symplectic group . The cohomological dimension of the group equals to . The main goal of the present paper is to compute the top homology group of the Torelli group in the case as ‐module. We prove an isomorphism where is the quotient of by its diagonal subgroup with the natural action of the permutation group (the action of is trivial). We also construct an explicit set of generators and relations for the group .