collaborators

6 papers

math.GT2026

Gröbner Bases for Alexander Fitting Ideals of Links

Takefumi Nosaka, Kotaro Shimizu

Multivariable Alexander theory produces Fitting ideals without preferred generators. After fixing a coefficient field and a monomial order, we represent these ideals by reduced Grö…

math.GT2026

Type Annihilation for Classifying Maps of Rack Spaces

Takefumi Nosaka

We study the classifying map $c\colon BX\to K(\As(X),1)$ of a rack of finite type. Let $t = \Type(X)$. We prove that for every when is connected, and t…

math.GT2026

Meta-nilpotent knot invariants and symplectic automorphism groups of free nilpotent groups

Takefumi Nosaka

We develop nilpotently -localization of knot groups in terms of the (symplectic) automorphism groups of free nilpotent groups. We show that any map from the set of conjugacy cla…

math.GT2026

Chern--Simons-type -cocycles and -torsion in the third homology of discrete diffeomorphism groups

Takefumi Nosaka

We prove that the third integral group homology of both the volume-preserving diffeomorphism group and the strict contactomorphism group of the standard \(3\)-sphere contains \((\m…

math.GT2024

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 i…

math.GT2024

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…