Algebra/Topology seminar

Speaker: Filippos Sytilidis

Title: Surgery Presentations of Bordism Bicategories

Abstract: Topological quantum field theories (TQFTs) are symmetric monoidal functors from bordism categories to categories of vector spaces. Classifying low-dimensional TQFTs often relies on presenting bordism categories in terms of generators and relations. This talk introduces these ideas and outlines a general procedure for constructing such presentations using Morse–Cerf theory and surgery. The approach further extends to the setting of bordism (2,1)-categories. As an application, I will describe an explicit finite presentation of the three-dimensional bordism (2,1)-category.