10 papers
The half-monochromatic colorings of plane graphs with even polygonal faces
Kazuhiro Ichihara, Yuha Tamura
On the maximum number of colors for proper anti-rainbow colorings on a planar quadrangulation, an upper bound was given by Enami-Ozeki-Yamaguchi in terms of the independence number…
Finiteness of purely cosmetic fillings
Kazuhiro Ichihara
A pair of Dehn fillings on a compact, orientable 3-manifold with a torus boundary is said to be purely cosmetic if the resulting 3-manifolds are orientation-preservingly homeomorph…
Degeneracy slopes, boundary slopes and exceptional surgery slopes
Kazuhiro Ichihara
We give an upper bound on the distance between a degeneracy slope for a very full essential lamination and a boundary slope of an essential surface embedded in a compact, orientabl…
Euclidean lengths and the Culler-Shalen norms of slopes
Kazuhiro Ichihara
In the study of exceptional Dehn fillings, two functions on slopes, called the Euclidean length on a horotorus and the Culler-Shalen norm, play important roles. In this paper, we i…
Hyperbolic small knots in spherical manifolds
Kazuhiro Ichihara
It was conjectured by Lopez that every closed irreducible non-Haken 3-manifold contains a small knot. In this paper, we give explicit examples of hyperbolic small knots in most clo…
Pure cactus groups and configuration spaces of points on the circle
Takatoshi Hama, Kazuhiro Ichihara
In this article, we provide a summary of the results presented in the previous two papers of the authors and in the second author's Master thesis, which concern pure cactus groups…
A presentation of the pure cactus group of degree four
Takatoshi Hama, Kazuhiro Ichihara
We give a simple presentation of the pure cactus group of degree four. This presentation is obtained by considering an action of on the hyperbolic plane and construct…
A note on the pure cactus group of degree three and the configuration space of four points on the circle
Takatoshi Hama, Kazuhiro Ichihara
The cactus group was introduced by Henriques and Kamnitzer as an analogue of the braid group. In this note, we provide an explicit description of the relationship between the pure…
On two-bridge ribbon knots
Sayo Horigome, Kazuhiro Ichihara
We show that a two-bridge ribbon knot with and admits a symmetric union presentation with partial knot which is a two-bridge knot …
Boundary slopes (nearly) bound exceptional slopes
Kazuhiro Ichihara, Thomas W. Mattman
For a hyperbolic knot in , Dehn surgery along slope $r \in \Q \cup \{\frac10\}$ is {\em exceptional} if it results in a non-hyperbolic manifold. We say meridional surgery, $r…