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math.GT2023
The Dijkgraaf-Witten invariants from second Chern classes
Takefumi Nosaka
Given a 3-cocycle in the cohomology of a finite group , we can define the Dijkgraaf-Witten invariant of closed 3-manifolds. In this paper, we focus on the case where is…
math.GT2023
Nonacyclic Reidemeister torsions of manifolds of odd dimension
Takefumi Nosaka, Koki Yanagida, Naoko Wakijo
Given an oriented closed manifold of odd dimension and a unitary representation $ρ: π_1(M) \ra \GL_n(\F)$, we define a Reidemeister torsion, even if the cohomology associated w…
math.GT2023
Skew-rack cocycle invariants of closed 3-manifolds
Takefumi Nosaka
We establish a new approach to obtain 3-manifold invariants via Dehn surgery. For this, we introduce skew-racks with good involution and Property FR, and define cocycle invariants…