PIRSA:24030091 Conference Condensed Matter

DOI10.48660/24030091

Conference/School: Higher Categorical Tools for Quantum Phases of Matter

Johnson-Freyd, T. (2024). Quantum homotopy groups. Perimeter Institute. https://pirsa.org/24030091

Johnson-Freyd, Theo. Quantum homotopy groups. Perimeter Institute, Mar. 21, 2024, https://pirsa.org/24030091 

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

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.

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