8 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…
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…