10 papers
Asymmetric L-space knots with arbitrary braid index
Keisuke Himeno, Masakazu Teragaito
The first examples of asymmetric L-space knots were found by Baker and Luecke. Among Baker-Luecke knots, the simplest one has braid index 12. Later, it turned out that there are ju…
A condition of admissibility for generalized Alexander quandles
Katsunori Arai, Keisuke Himeno, Ryoya Kai +1
A typical example of a quandle is the conjugation quandle. A quandle is said to be admissible if it is isomorphic to a conjugation quandle. We study the admissibility problem for q…
The bridge index and the braid index for twist positive knots
Keisuke Himeno
In general, the bridge index of a knot is less than or equal to its braid index. A natural question is when these two values coincide. Motivated by a conjecture of Krishna and Mort…
Non-braid positive hyperbolic -space knots
Keisuke Himeno
An -space knot is a knot that admits a positive Dehn surgery yielding an -space. Many known hyperbolic -space knots are braid positive, meaning they can be represented as…
The unoriented band unknotting numbers of torus knots
Keisuke Himeno
The unoriented band unknotting number of a knot is the minimum number of oriented or non-oriented band surgeries that turn the knot into the unknot. Batson introduced a certain non…
Hyperbolic knots with arbitrarily large torsion order in knot Floer homology
Keisuke Himeno, Masakazu Teragaito
In knot Floer homology, there are two types of torsion order. One is the minimal power of the action of the variable to annihilate the -torsion submodule of th…
Twisted right-angled Artin groups embedded in knot groups
Keisuke Himeno, Masakazu Teragaito
Twisted right-angled Artin groups are defined through presentation based on mixed graphs. Each vertex corresponds to a generator, each undirected edge yields a commuting relation a…
Classification of generalized torsion elements of order two in 3-manifold groups
Keisuke Himeno, Kimihiko Motegi, Masakazu Teragaito
Let be a group and a non-trivial element in . If some non-empty finite product of conjugates of equals to the identity, then is called a generalized torsion elem…
New family of hyperbolic knots whose Upsilon invariants are convex
Keisuke Himeno
The Upsilon invariant of a knot is a concordance invariant derived from knot Floer homology theory. It is a piecewise linear continuous function defined on the interval . Bo…
Generalized torsion, unique root property and Baumslag--Solitar relation for knot groups
Keisuke Himeno, Kimihiko Motegi, Masakazu Teragaito
Let be a group. If an equation in implies for any elements and , then is called an --group. It is completely understood which knot groups…