Quantum homotopy groups

          @misc{ scivideos_PIRSA:24030091,
            doi = {10.48660/24030091},
            url = {https://pirsa.org/24030091},
            author = {Johnson-Freyd, Theo},
            keywords = {Quantum Matter},
            language = {en},
            title = {Quantum homotopy groups},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2024},
            month = {mar},
            note = {PIRSA:24030091 see, \url{https://scivideos.org/index.php/pirsa/24030091}}
          }
          

Abstract

An *open-closed tqft* is a tqft with a choice of boundary condition. Example: the sigma model for a sufficiently finite space, with its Neumann boundary. Slogan: every open-closed tqft is (sigma model, Neumann boundary) for some “quantum space”. In this talk, I will construct homotopy groups for every such “quantum space” (and recover usual homotopy groups). More precisely, these “groups” are Hopf in some category. Given a “quantum fibre bundle” (a relative open-closed tqft), I will construct a Puppe long exact sequence. Retracts in 3-categories and a higher Beck-Chevalley condition will make appearances. This project is joint work in progress with David Reutter.