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Bordism invariants of the mapping class group

By Aaron Heap


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 homomorphisms, the Birman-Craggs homomorphisms, and the Morita homomorphisms

Topics: Mathematics
Year: 2004
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