Title: Crossed module graded categories and state-sum homotopy invariants of maps
Speaker: Kursat Sozer (McMaster University)
Abstract: In topology, groups serve as algebraic models for 1-types, which are spaces with vanishing second and higher homotopy groups. Crossed modules, on the other hand, generalize groups and are useful for modeling 2-types. In this talk, we will introduce the concept of a crossed module graded fusion category, which is a generalization of a fusion category graded by a group. We will then use these categories to construct a 3-dimensional state-sum homotopy quantum field theory (HQFT) with a 2-type target. Such an HQFT assigns a scalar to a map defined from a closed oriented 3-manifold to the fixed 2-type and this scalar is invariant under homotopies. Our construction generalizes the state-sum Turaev-Virelizier HQFT with an aspherical target. This is joint work with Alexis Virelizier.
URL associated with Seminar: https://www.asc.ohio-state.edu/math/vqss/