Matthew Cellot (University of Lille) – Extensions of fusion 2-categories and quantum homotopy invariants of 4-manifolds (Part 2)
- Date
- @ MALL, online, 15:00
- Location
- MALL, online
- Speaker
- Matthew Cellot
- Affiliation
- University of Lille
- Category
- Algebra
Abstract - A fundamental notion in quantum topology is that of topological quantum field theory (TQFT) formulated by Witten and Atiyah. This notion originates in ideas from quantum physics and constitutes a framework that organizes certain topological invariants of manifolds, called quantum invariants, which are defined by means of quantum groups.
Homotopy quantum field theories (HQFTs) are a generalization of TQFTs. The idea is to use TQFT techniques to study principal bundles over manifolds and, more generally, homotopy classes of maps from manifolds to a (fixed) topological space called the target. The resulting invariants are called quantum homotopy invariants.
Turaev and Virelizier have constructed quantum homotopy invariants of 3-manifolds (by state sum) when the target space is a 1-type, and Sözer and Virelizier have recently constructed quantum homotopy invariants of 3-manifolds when the target space is a 2-type. Using state sum techniques, Douglas and Reutter have constructed quantum invariants of 4-manifolds using fusion 2-categories. In this talk, we combine both of these approaches: we construct quantum homotopy invariants of 4-manifolds with a 3-type target from 3-group extensions of fusion 2-categories.