Eclipses on Zippers

KyeongRo Kim

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arXiv · 2604.21792

Eclipses on Zippers

KyeongRo Kim

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Abstract

Calegari and Loukidou introduced zippers, consisting of a disjoint pair of invariant real trees in the boundary of a closed hyperbolic 3-manifold group $\pi_1(M)$, which ensure the existence of a universal circle. We study the action of $\pi_1(M)$ 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.

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BibTeX RIS

KyeongRo Kim. 2026-04-23. Eclipses on Zippers. https://arxiv.org/abs/2604.21792

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