6 papers
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…
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…
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…
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…
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…
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 $Ï: Ï_1(M) \ra \GL_n(\F)$, we define a Reidemeister torsion, even if the cohomology associated…