Dijkgraaf-Witten invariant in topological $K$-theory

Koki Yanagida

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arXiv · 2502.11548

Dijkgraaf-Witten invariant in topological $K$-theory

Koki Yanagida

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Abstract

Given a finite group $G$, we define a new invariant of odd-dimensional oriented closed manifolds and call it the KDW invariant. This invariant is a Dijkgraaf--Witten invariant in terms of $K$-theory. In this paper, we compute the invariant of the Brieskorn homology spheres with $G=\mathrm{PSL}_2(\mathbb{F}_p)$. We should remark that, in this computational result, the fundamental groups of the Brieskorn homology spheres and $\mathrm{PSL}_2(\mathbb{F}_p)$ are not nilpotent.

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BibTeX RIS

Koki Yanagida. 2025-02-17. Dijkgraaf-Witten invariant in topological $K$-theory. https://arxiv.org/abs/2502.11548

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