Bordism Invariants of the Mapping Class Group

Details Bordism Invariants of the Mapping Class Group Bordism Invariants of the Mapping Class Group

2005-02-28

arxiv.org/abs/math/0502587v1

Mathematics

Geometric Topology

34 pages, 7 figures

Scientific paper

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.

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