Cochran, Tim D.2009-06-042009-06-042004Heap, Aaron. "Bordism invariants of the mapping class group." (2004) Diss., Rice University. <a href="https://hdl.handle.net/1911/18635">https://hdl.handle.net/1911/18635</a>.https://hdl.handle.net/1911/18635We 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.70 p.application/pdfengCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.MathematicsThesisTHESIS MATH. 2004 HEAP