A generalization of Dijkgraaf–Witten theory

The main purpose of this paper is to give a generalization of Dijkgraaf–Witten theory. We construct a TQFT for $E$-oriented manifolds using a pairing of spectra $\mu : E \wedge F \to G$ and a representative of an $F$-cohomology class of the classifying space of a finite group. If $E = H\mathbb{Z}, F = G = HU(1)$ and the pairing is induced by the $\mathbb{Z}$-module structure of $U(1)$, then the TQFT reproduces Dijkgraaf–Witten theory. For the case that each of spectra $E, F,G$ is given as the $K$-theory spectrum $KU$, we further generalize our construction based on non-commutative settings.

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Published 25 March 2024