%0 Journal Article
%T Bordism Invariants of the Mapping Class Group
%A Aaron Heap
%J Mathematics
%D 2005
%I arXiv
%X We define new bordism and spin bordism invariants of certain subgroups of the mapping class group of a surface. In particular, they are invariants of the Johnson filtration of the mapping class group. The second and third terms of this filtration are the well-known Torelli group and Johnson subgroup, respectively. We introduce a new representation in terms of spin bordism, and we prove that this single representation contains all of the information given by the Johnson homomorphism, the Birman-Craggs homomorphism, and the Morita homomorphism.
%U http://arxiv.org/abs/math/0502587v1