Kevin Walker

Kevin Walker, Microsoft Station Q

I’ll describe two approaches to constructing a universal state sum. The first approach (arXiv:2104.02101) is more elementary and assumes semisimplicity. Special cases of this state sum include Turaev–Viro, Crane–Yetter, Douglas–Reutter, the Reshetikhin–Turaev Dehn surgery formula (thought of as a state sum), Brown–Arf for $\mathrm{Pin}_-$ 2-manifolds, and Dijkgraaf–Witten. The second approach (joint work with David Reutter) is more general and does not assume semisimplicity. If there’s time I’ll sketch a program to use the non-semisimple state sum to reproduce a cluster of non-semi-simple 3-manifold invariants due to many different authors (Lyubashenko, Kuperberg, Hennings, ... Geer, Gainutdinov, Patureau-Mirand, ... ).