Bordism invariants of the mapping class group

• Main Author: Heap, Aaron
• Other Authors: Cochran, Tim D.
• Format: Others
• Language: English
• Published: 2009
• Subjects: Mathematics
• Online Access: http://hdl.handle.net/1911/18635

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.