Dijkgraaf-Witten invariant in topological K-theory

2025/02/17 by Koki Yanagida, Yanagida, Koki
Mathematics · #55N15 #FOS: Mathematics #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2502.11548

openalex publication_date 2025/02/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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=PSL₂(\mathbbF_p). We should remark that, in this computational result, the fundamental groups of the Brieskorn homology spheres and PSL₂(\mathbbF_p) are not nilpotent.

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