11 papers
An example of biquandle and an invariant of long virtual knots defined through it
Nozomu Sekino
We introduce an example of biquandle and define an invariant of long virtual knots through it. As an application, we give a necessary condition for two long virtual knots commuting…
An example of semiquandle and u-polynomials for flat virtual knots via this semiquandle coloring
Nozomu Sekino
Flat virtual links are some variant of links, and semiquandles are counterparts of quandles or biquandles, which axiomize the Reidemeister-like moves. In this paper, we give some e…
On the Invalidity of Lemma 2.5 in our previous work on the Powell Conjecture
Sangbum Cho, Yuya Koda, Jung Hoon Lee +1
In our previous version entitled ``The reducing sphere complexes for the 3-sphere are connected: a proof of the Powell Conjecture", we claimed to prove the Powell Conjecture, which…
The JSJ-decomposition of the 3-manifold obtained by 0-surgery along a classical pretzel knot of genus one
Nozomu Sekino
We consider the JSJ-decomposition of the 3-manifold obtained by 0-surgery along a classical pretzel knot of genus one. We use the classification of exceptional fillings of minimall…
Generalized torsion elements in the fundamental groups of 3-manifolds obtained by the 0-surgeries along some double twist knots
Nozomu Sekino
We consider the 3-manifold obtained by the 0-surgery along a double twist knot. We construct a candidate for a generalized torsion element in the fundamental group of the surged ma…
The subgroup of the Goeritz group of the Heegaard splitting induced by an openbook decomposition consisting of elements preserving the binding
Nozomu Sekino
When a 3-manifold admits an openbook decomposition, we get a Heegaard splitting by thickening a page. This splitting surface has a special multi curves coming from the binding. In…
The Goeritz group of a Heegaard splitting of genus two of a Seifert manifold whose base orbifold is sphere with three exceptional points of sufficiently complex coefficients
Nozomu Sekino
In this paper, we add examples to Goeritz groups, the mapping class groups of given Heegaard splittings of 3-manifolds. We focus on a Heegaard splitting of genus two of a Seifert m…
Generalized torsions in once punctured torus bundles
Nozomu Sekino
A generalized torsion in a group, an non-trivial element such that some products of its conjugates is the identity. This is an obstruction for a group being bi-orderable. Though it…
The existence of homologically fibered links and solutions of some equations
Nozomu Sekino
There is one generalization of fibered links in 3-manifolds, called homologically fibered links. It is known that the existence of homologically fibered links whose fiber surface h…
Lens spaces which are realizable as closures of homology cobordisms over planar surfaces
Nozomu Sekino
We determine the condition on a given lens space having a realization as a closure of homology cobordism over a planar surface with a given number of boundary components. As a coro…
Genus one fibered knots in 3-manifolds with reducible genus two Heegaard splittings
Nozomu Sekino
We give a necessary and sufficient condition for a simple closed curve on the boundary of a genus two handlebody to decompose the handlebody into (torus with one boundary component…