9 citations · 40 across the 33 of their papers we have counts for
32 papers · 1 filter
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…
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 is…
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…
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…
Reciprocity of the Chern-Simons invariants of 3-manifolds
Takefumi Nosaka
We pose reciprocity conjectures of the Chern-Simons invariants of 3-manifolds, and discuss some supporting evidence on the conjectures. Especially, we show that the conjectures hol…
A solvable extended logarithm of the Johnson homomorphism
Takefumi Nosaka
We suggest an extension of a certain logarithm of the total Johnson map in terms of solvable Lie groups. Here, the domain of the map is extended to a subset consisting of exponenti…
Fox pairings of Poincaré duality groups
Takefumi Nosaka
This paper develops the study of Fox pairings of a group from the viewpoint of group cohomology. We compute some cohomology groups of Fox pairings of , where admits a Po…
Goldman-type Lie algebras from knots
Takefumi Nosaka
We define Lie algebras from a class of knots in a homology 3-sphere. Since the definitions in terms of group homology are analogous to Goldman Lie algebra \cite{Gold}, we discuss r…
Cellular chain complexes of universal covers of some 3-manifolds
Takefumi Nosaka
For a closed 3-manifold in a certain class, we give a presentation of the cellular chain complex of the universal cover of . The class includes all surface bundles, some sur…
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…
Some comparisons of Blanchfield pairings and cohomology pairings of knots
Takefumi Nosaka
We study some comparison between a bilinear cohomology pairing in local coefficients and the Blanchfield pairing of a knot. We show that the former pairing is an -equivalent inv…
An -Casson invariant and Reidemeister torsions
Takefumi Nosaka
We define an -Casson invariant of closed 3-manifolds. We also observe procedures of computing the invariants in terms of Reidemeister torsions. We discuss some ap…
Twisted Alexander invariants of knot group representations II; computation and duality
Takefumi Nosaka
Given a homomorphism from a link group to a group, we introduce a -class in another way, which is a generalization of the 1-variable Alexander polynomial. We compare the …
Twisted Alexander invariants of knot group representations
Takefumi Nosaka
Given a homomorphism from a knot group to a fixed group, we introduce an element of a -group, which is a generalization of (twisted) Alexander polynomials. We compare this $K_…
Meta-nilpotent quotients of mapping-torus groups and two topological invariants of quadratic forms
Takefumi Nosaka
We determine the center of a meta-nilpotent quotient of a mapping-torus group. As a corollary, we introduce two invariants, which are quadratic forms, of knots and of mapping class…
Schur Multipliers and Second Quandle Homology
Rhea Palak Bakshi, Dionne Ibarra, Sujoy Mukherjee +2
We define a map from second quandle homology to the Schur multiplier and examine its properties. Furthermore, we express the second homology of Alexander quandles in terms of exter…
Twisted cohomology pairings of knots III; triple cup products
Takefumi Nosaka
Given a representation of a link group, we introduce a trilinear form, as a topological invariant. We show that, if the link is either hyperbolic or a knot with malnormality, then…
de Rham theory and cocycles of cubical sets from smooth quandles
Takefumi Nosaka
We show a de Rham theory for cubical manifolds, and study rational homotopy type of the classifying spaces of smooth quandles. We also show that secondary characteristic classes in…
Milnor-Orr invariants from the Kontsevich invariant
Takefumi Nosaka
As nilpotent studies in knot theory, we focus on invariants of Milnor, Orr, and Kontsevich. We show that the Orr invariant of degree is equivalent to the tree reduction of th…
Milnor invariants via unipotent Magnus embeddings
Hisatoshi Kodani, Takefumi Nosaka
We reconfigure the Milnor invariant of links in terms of central group extensions and unipotent Magnus embeddings. We also develop a diagrammatic computation of the invariant and c…
Cocycles of nilpotent quotients of free groups
Takefumi Nosaka
We focus on the cohomology of the -th nilpotent quotient of the free group, . This paper describes all the group 2-, 3-cocycles in terms of Massey products, and gives exp…
Bilinear-form invariants of Lefschetz fibrations over the 2-sphere
Takefumi Nosaka
We introduce invariants of Hurwitz equivalence classes with respect to arbitrary group . The invariants are constructed from any right -modules and any -invariant bili…