Topology Seminar (Introductory Talk): Pontryagin-Thom as a bridge from homotopy to (higher) categories

Seminar | March 15 | 2:10-3 p.m. | 736 Evans Hall

 Chris Schommer-Pries, Notre Dame

 Department of Mathematics

Grothendieck's homotopy hypothesis asserts that for a good theory of higher categories there should be an equivalence between homotopy n-types and n-groupoids and hence standard tools and techniques for understanding homotopy types have categorical significance. In this talk I will describe how the Pontryragin-Thom construction can be used in this way. We will see for example that free braided monoidal Picard category is equivalent to a certain bordism category of framed tangles. Other examples relevant to the second talk will also be described.