A generalization of Dijkgraaf-Witten theory

TL;DR

This paper generalizes Dijkgraaf-Witten theory by constructing a TQFT for E-oriented manifolds using spectra morphisms, extending to non-commutative K-theory spectra for broader applications.

Contribution

It introduces a new framework for TQFTs based on spectra morphisms and extends the theory to non-commutative K-theory spectra, broadening its scope.

Findings

Constructed a TQFT for E-oriented manifolds using spectra morphisms.

Generalized the theory to non-commutative K-theory spectra.

Provided a unifying framework for Dijkgraaf-Witten theory and its extensions.

Abstract

The main purpose of this paper is to give a generalization of Dijkgraaf-Witten theory. Consider a morphism from a smash product of spectra E,F to another spectrum G. We construct a TQFT for E-oriented manifolds using a representative of an F-cohomology class of the classifying space of a finite group. 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.