Bordism Invariants of the Mapping Class Group
Geometric Topology
2007-05-23 v1 Algebraic Topology
Abstract
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.
Cite
@article{arxiv.math/0502587,
title = {Bordism Invariants of the Mapping Class Group},
author = {Aaron Heap},
journal= {arXiv preprint arXiv:math/0502587},
year = {2007}
}
Comments
34 pages, 7 figures