Survey of 3-Dimensional TQFTs and Quantum Invariants of 3-Manifolds

Abstract: In this talk, I will give a gentle overview of 3-dimensional topological quantum field theories (TQFTs) and the corresponding quantum invariants of closed 3-manifolds. After briefly recalling essential algebraic notions such as pivotal, fusion, and modular categories, I will describe the two main constructions of 3-dimensional TQFTs: the surgery approach (Witten–Reshetikhin–Turaev invariants) and the state-sum approach (Turaev–Viro–Barrett–Westbury invariants). I will then summarize the key comparison result involving the categorical center construction, illustrating how these two approaches yield isomorphic TQFTs. If time permits, I will close by briefly mentioning extensions to homotopy quantum field theories (HQFTs) and highlight some recent developments in this direction.

algebraic topologycategory theory

Audience: researchers in the topic

Bilkent Topology Seminar

Series comments: Contact the organizer to get access to Zoom.

Recordings of talks available at www.youtube.com/channel/UCLrmyGpqxyeVpTcA1b5HcMw/videos