CAT(0) property and hyperbolicity of affine cactus groups
We show that the affine cactus group is a CAT$(0)$ group for all degrees. Furthermore, we show that the affine cactus group $AJ_3$ of degree three is a hyperbolic group.
math.GR↗
arXiv subjects
Takatoshi Hama
Publications and source records attributed to Takatoshi Hama.
Pure cactus groups and configuration spaces of points on the circle
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 and configuration spaces of points on the circle.
math.GT↗
A presentation of the pure cactus group of degree four
We give a simple presentation of the pure cactus group $PJ_4$ of degree four. This presentation is obtained by considering an action of $PJ_4$ on the hyperbolic plane and constructing a Dirichlet polygon for the action. As a corollary, we provide a direct alternative proof that $PJ_4$ is isomorphic to the fundamental group of the connected sum of five real projective planes.
math.GR↗
A note on the pure cactus group of degree three and the configuration space of four points on the circle
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 cactus group of degree three and the configuration space of four points on the circle.
math.GR↗