Advances in Theoretical and Mathematical Physics
Volume 26 (2022)
Number 10
A generalization of Dijkgraaf–Witten theory
Pages: 3677 – 3719
DOI: https://dx.doi.org/10.4310/ATMP.2022.v26.n10.a7
Author
Minkyu Kim (Graduate School of Mathematical Sciences, University of Tokyo, Japan; and Korean Institute for Advanced Study, Seoul, South Korea)
Abstract
The main purpose of this paper is to give a generalization of Dijkgraaf–Witten theory. We construct a TQFT for -oriented manifolds using a pairing of spectra and a representative of an -cohomology class of the classifying space of a finite group. If and the pairing is induced by the -module structure of , then the TQFT reproduces Dijkgraaf–Witten theory. For the case that each of spectra is given as the -theory spectrum , we further generalize our construction based on non-commutative settings.
Published 25 March 2024