Topology Seminar (Main Talk): A complete model for the cobordism category

Seminar | May 1 | 4:10-5 p.m. | 3 Evans Hall

 Claudia Scheimbauer, NTNU

 Department of Mathematics

Lurie’s approach to the Cobordism Hypothesis builds upon a suitable higher category of cobordisms. The model of \((\infty,1)\)-categories given by complete Segal spaces (and their higher analogs) are a very natural choice for constructing cobordism categories. A drawback is that the first natural definitions only give Segal spaces, which, for high dimensions, are not complete. This follows directly from the \(s\)-cobordism theorem. In this talk, after explaining and defining the necessary notions in detail, I will explain a very simple model of cobordisms, which is a completion of the usual one. In particular it indeed is complete. This is joint work with Ulrike Tillmann.