8 papers
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…
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…
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…
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…
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…
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…