Logo

Mathematical Sciences Research Institute

Home » HC & QS - Graduate Student Seminar: About lines and circles: the bordism category in dimension 1 & Frobenius algebras and embedded surfaces

Seminar

HC & QS - Graduate Student Seminar: About lines and circles: the bordism category in dimension 1 & Frobenius algebras and embedded surfaces February 28, 2020 (12:30 PM PST - 01:30 PM PST)
Parent Program:
Location: MSRI: Baker Board Room
Speaker(s) Jan Steinebrunner (University of Oxford), Dominic Weiller (Australian National University)
Description No Description
Video
No Video Uploaded
Abstract/Media

Abstract for Jan Steinbrunner:

The 1-dimensional bordism category Cob_1 is easily defined: objects are finite oriented sets and morphisms are diffeomorphism classes of 1-dimensional bordisms, in other words: lines and circles. A close relative of Cob_1 is the (infinity,1)-category Bord_1. This is a more fancy version of Cob_1 where we don't identify diffeomorphic bordisms, but rather assemble them in an appropriate moduli space. I will recall both of these categories and how they are related. Then I'll explain why essentially the only difference between the two are the rotations of the circle, and how to make this statement precise. Finally, I'll use the universal property Bord_1 enjoys because of the cobordism hypothesis to compute the classifying space of Cob_1. Afterwards we can also talk about how to do this in dimension 2, how this relates to topological cyclic homology of \Omega X, or about any other questions that come up during the talk.

No Notes/Supplements Uploaded No Video Files Uploaded