Dijkgraaf-Witten invariant in topological $K$-theory

Koki Yanagida

Dijkgraaf-Witten invariant in topological $K$-theory

Geometric Topology 2025-02-18 v1

Authors: Koki Yanagida

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.

Keywords

Dijkgraaf-Witten invariant topological K-theory Brieskorn homology spheres PSL_2(F_p) fundamental group

Cite

@article{arxiv.2502.11548,
  title  = {Dijkgraaf-Witten invariant in topological $K$-theory},
  author = {Koki Yanagida},
  journal= {arXiv preprint arXiv:2502.11548},
  year   = {2025}
}

Comments

27 pages. To appear in Kodai Mathematical Journal

Dijkgraaf-Witten invariant in topological $K$-theory

Abstract

Keywords

Cite

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