arXiv subjects

Ken'ichi Yoshida

Publications and source records attributed to Ken'ichi Yoshida.

15 recordsLinked to original sources

arXiv2026

On Isotopies and hyperbolicity of weaves

A weave is a type of textile that consists of vertical and horizontal threads, and typically it has a periodic structure. In this paper, we regard a weave as a link in the thickened torus with a diagram consisting of closed geodesics. As main results, we characterize isotopies and hyperbolicity of weaves to determine them from diagrams. Moreover, we show that there does not exist an essential Conway sphere for a weave. We use normal positions of essential surfaces of weave complements to describe them.

math.GT↗

arXiv2026

Uniqueness of free 2-periodicities of links

We show that if two links in the real projective 3-space $\mathbb{RP}^{3}$ have isotopic preimages in the 3-sphere $S^{3}$ by the double covering map, then they are themselves isotopic in $\mathbb{RP}^{3}$.

math.GT↗

arXiv2026

On the isotopies of tangles in periodic 3-manifolds using finite covers

A periodic tangle is a one-dimensional submanifold in $\mathbb{R}^3$ that has translational symmetry in one, two or three transverse directions. A periodic tangle can be seen as the universal cover of a link in the solid torus, the thickened torus, or the three-torus, respectively. Our goal is to study equivalence relations of such periodic tangles. Since all finite covers of a link lift to the same periodic tangle, it is necessary to prove that isotopies between different finite covers are preserved. In this paper, we show that if two links have isotopic lifts in a common finite cover, then they are isotopic. To do so, we employ techniques from 3-manifold topology to study the complements of such links.

math.GT↗

arXiv2025

Linking numbers for periodic tangles

Periodic tangles are 1-dimensional submanifolds in the 3-space with translational symmetry. In this paper, we define the linking numbers for singly, doubly, and triply periodic tangles using appropriate motifs and show that they are well-defined and invariant under link-homotopy. Furthermore, we extend the notion to the higher order linking numbers for singly periodic tangles.

math.GT↗

arXiv2025

Chiral Analogues of Knit Stitches Designed Using Chiral Topology

Fabrics are flexible thin structures made of entangled yarn or fibers, yet the topological bases of their mechanics remain poorly understood. For weft knitted fabrics, we describe how the entanglement of adjacent stitches contributes to the flexibility of the fabric. Interpreting heterogeneous stitch pairs as domain boundaries reveals that the step between pairs of neighboring stitches is responsible for direction-specific flexibility. In typical knitted fabrics, anisotropic flexibility can be attributed to latticed domain boundaries. The intersections between domain boundaries result in point defects that induce frustration that resembles the impossible Penrose stairs. We identify these by a chiral characteristic, defined summing the ascending or descending steps in a cycle surrounding the defect. Remarkably, seed fabric, a knit with high flexibility in both course and wale directions, is characterized as a racemic crystal of these chiral point defects.

cond-mat.soft↗

arXiv2025

Links in the spherical 3-manifold obtained from the quaternion group and their lifts

We show that there are infinitely many triples of non-isotopic hyperbolic links in the lens space $L(4,1)$ such that the three lifts of each triple in $S^{3}$ are isotopic. They are obtained as the lifts of links in $S^{3} / Q_{8}$ by double covers, where $Q_{8}$ is the quaternion group. To construct specific examples, we introduce a diagram of a link in $S^{3} / Q_{8}$ obtained by projecting to a square. The diagrams of isotopic links are connected by Reidemeister-type moves.

math.GT↗

arXiv2025

Holed cone structures on 3-manifolds

We introduce holed cone structures on 3-manifolds to generalize cone structures. In the same way as a cone structure, a holed cone structure induces the holonomy representation. We consider the deformation space consisting of the holed cone structures on a 3-manifold whose holonomy representations are irreducible. This deformation space for positive cone angles is a covering space on a reasonable subspace of the character variety.

math.GT↗

arXiv2024

A mathematical approach to mechanical properties of networks in thermoplastic elastomers

We employ a mathematical model to analyze stress chains in thermoplastic elastomers (TPEs) with a microphase-separated spherical structure composed of triblock copolymers. The model represents stress chains during uniaxial and biaxial extensions using networks of spherical domains connected by bridges. We advance previous research and discuss permanent strain and other aspects of the network. It explores the dependency of permanent strain on the extension direction, using the average of tension tensors to represent isotropic material behavior. The concept of deviation angle is introduced to measure network anisotropy and is shown to play an essential role in predicting permanent strain when a network is extended in a specific direction. The paper also discusses methods to create a new network structure using various polymers.

cond-mat.soft↗

arXiv2022

Degeneration of 3-dimensional hyperbolic cone structures with decreasing cone angles

For 3-dimensional hyperbolic cone structures with cone angles $θ$, local rigidity is known for $0 \leq θ\leq 2π$, but global rigidity is known only for $0 \leq θ\leq π$. The proof of the global rigidity by Kojima is based on the fact that hyperbolic cone structures with cone angles at most $π$ do not degenerate in deformations decreasing cone angles to zero. In this paper, we give an example of a degeneration of hyperbolic cone structures with decreasing cone angles less than $2π$. These cone structures are constructed on a certain alternating link in the thickened torus by gluing four copies of a certain polyhedron. For this construction, we explicitly describe the isometry types on such a hyperbolic polyhedron.

math.GT↗

arXiv2022

A mathematical model of network elastoplasticity

We introduce a mathematical model, based on networks, for the elasticity and plasticity of materials. We define the tension tensor for a periodic graph in a Euclidean space, and we show that the tension tensor expresses elasticity under deformation. Plasticity is induced by local moves on a graph. The graph is described in terms of the weights of edges, and we discuss how these weights affect the plasticity.

math.DG↗

arXiv2022

Quotient topology on the set of commensurability classes of hyperbolic 3-manifolds

We investigate relation between Dehn fillings and commensurability of hyperbolic 3-manifolds. The set consisting of the commensurability classes of hyperbolic 3-manifolds admits the quotient topology induced by the geometric topology. We show that this quotient space satisfies some separation axioms. Roughly speaking, this means that commensurablity classes are sparsely distributed in the space consisting of the hyperbolic 3-manifolds.

math.GT↗

arXiv2019

Unions of 3-punctured spheres in hyperbolic 3-manifolds

We classify the topological types for the unions of the totally geodesic 3-punctured spheres in orientable hyperbolic 3-manifolds. General types of the unions appear in various hyperbolic 3-manifolds. Each of the special types of the unions appears only in a single hyperbolic 3-manifold or Dehn fillings of a single hyperbolic 3-manifold. Furthermore, we investigate bounds of the moduli of adjacent cusps for the union of linearly placed 3-punctured spheres.

math.GT↗

arXiv2018

Stable presentation length of 3-manifold groups

We introduce the stable presentation length of a finitely presented group. The stable presentation length of the fundamental group of a 3-manifold can be considered as an analogue of the simplicial volume. We show that the stable presentation length have some additive properties like the simplicial volume, and the simplicial volume of a closed 3-manifold is bounded from above and below by constant multiples of the stable presentation length of its fundamental group.

math.GT↗

arXiv2013

The minimal volume orientable hyperbolic 3-manifold with 4 cusps

We prove that the 8^4_2 link complement is the minimal volume orientable hyperbolic manifold with 4 cusps. Its volume is twice of the volume V_8 of the ideal regular octahedron, i.e. 7.32... = 2V_8. The proof relies on Agol's argument used to determine the minimal volume hyperbolic 3-manifolds with 2 cusps. We also need to estimate the volume of a hyperbolic 3-manifold with totally geodesic boundary which contains an essential surface with non-separating boundary.

math.GT↗

arXiv2006

Awaking of ferromagnetism in GaMnN through control of Mn valence

Room temperature ferromagnetism of GaMnN thin films is awaked by a mild hydrogenation treatment of samples synthesized by molecular beam epitaxy. Local environment of Mn atoms is monitored by Mn-L2,3 near edge x-ray absorption fine structure (NEXAFS) technique. Doped Mn ions are present at substitutional sites of Ga both before and after the hydrogenation. No secondary phase can be detected. Major valency of Mn changes from +3 to +2 by the hydrogenation. The present result supports the model that the ferromagnetism occurs when Mn2+ and Mn3+ are coexistent and holes in the mid- gap Mn band mediate the magnetic coupling.

cond-mat.mtrl-sci↗