Towards a finite presentation of the 3-dimensional bordism bicategory

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. We further discuss how this perspective can be extended to yield presentations of bordism bicategories. As an application, we will see an explicit finite presentation of the invertible part of the 3-dimensional bordism bicategory.