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math.GR2025
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…
math.GR2024
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…