A presentation of the pure cactus group of degree four
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908413026369536 |
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| author | Hama, Takatoshi Ichihara, Kazuhiro |
| author_facet | Hama, Takatoshi Ichihara, Kazuhiro |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_11852 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A presentation of the pure cactus group of degree four Hama, Takatoshi Ichihara, Kazuhiro Group Theory Geometric Topology 20F65, 20F38, 05E18, 57M60 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. |
| title | A presentation of the pure cactus group of degree four |
| topic | Group Theory Geometric Topology 20F65, 20F38, 05E18, 57M60 |
| url | https://arxiv.org/abs/2504.11852 |