Eclipses on Zippers
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866910160599908352 |
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| author | Kim, KyeongRo |
| author_facet | Kim, KyeongRo |
| contents | Calegari and Loukidou introduced zippers, consisting of a disjoint pair of invariant real trees in the boundary of a closed hyperbolic 3-manifold group $π_1(M)$, which ensure the existence of a universal circle. We study the action of $π_1(M)$ on a minimal zipper and prove a fixed point dichotomy: every nontrivial element either fixes a unique point in each tree or acts freely on both. This answers a question of Calegari and Loukidou. As a consequence, there exists an element with exactly one fixed point in each tree. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_21792 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Eclipses on Zippers Kim, KyeongRo Geometric Topology Dynamical Systems Group Theory Calegari and Loukidou introduced zippers, consisting of a disjoint pair of invariant real trees in the boundary of a closed hyperbolic 3-manifold group $π_1(M)$, which ensure the existence of a universal circle. We study the action of $π_1(M)$ on a minimal zipper and prove a fixed point dichotomy: every nontrivial element either fixes a unique point in each tree or acts freely on both. This answers a question of Calegari and Loukidou. As a consequence, there exists an element with exactly one fixed point in each tree. |
| title | Eclipses on Zippers |
| topic | Geometric Topology Dynamical Systems Group Theory |
| url | https://arxiv.org/abs/2604.21792 |