Title: What is Cobordism?
Speaker: Philip Egger
Speaker Info: 2nd Year Graduate Student
Given two oriented n-manifolds P and Q, we say that P and Q are cobordant if there exists an oriented (n+1)-manifold W with boundary the disjoint union of P and Q. This is an equivalence relation, and the set of classes forms a group. Using well-known results about cohomology of infinite real Grassmannians and the Thom spaces of the associated tautological bundles, we will see that this group is finite when n is not a multiple of 4. Furthermore, when n=4r, the group is finitely generated with rank p(r), the number of partitions of r.Date: Tuesday, November 08, 2011