6 papers · 1 filter
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…