Bordism Invariants of the Mapping Class Group

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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.
34 pages, 7 figures

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Geometric Topology, Algebraic Topology, 57M (Primary) 55 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/74346

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0502587
 http://arxiv.org/abs/math/0502587

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arXiv