4 papers
CAT(0) property and hyperbolicity of affine cactus groups
Takatoshi Hama
We show that the affine cactus group is a CAT group for all degrees. Furthermore, we show that the affine cactus group of degree three is a hyperbolic group.
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…
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 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…