Monday 27 May 2024
16:00–17:30*

Kürşat Sözer (McMaster University) — State-sum homotopy invariants of maps from 3-manifolds to 2-types

A 3-dimensional topological quantum field theory (TQFT) produces numerical invariants of closed 3-manifolds. Homotopy quantum field theories (HQFTs) generalize TQFTs by endowing manifolds with maps to fixed target space. In particular, for a connected CW complex X, a 3-dimensional HQFT with target X produces homotopy invariants of maps defined from closed 3-manifolds to X. In this talk, I will discuss such HQFT-invariants of maps and related algebraic structures when X is a homotopy 2-type, namely a topological space whose third and higher homotopy groups vanish. Specifically, we will use crossed modules as algebraic models for homotopy 2-types and construct state-sum invariants of maps from 3-manifolds to 2-types from crossed module graded spherical fusion categories. This joint work with Alexis Virelizier generalizes the state-sum Turaev-Virelizier HQFTs with aspherical targets.

* Eastern European Time, i.e. UTC+2 in winter and UTC+3 in summer.