Geometry and topology of closed geodesics complements in the 3-torus

José Andrés Rodríguez Migueles

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arXiv · 2412.03838

Geometry and topology of closed geodesics complements in the 3-torus

José Andrés Rodríguez Migueles

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Abstract

We show that for at most three closed geodesics with linearly independent directions, the homeomorphism type of its complement in the 3-torus is determine by the orbit of their direction vectors subspaces under the action of $PSL_3(\mathbb{Z}).$ Moreover, we provide asymptotically sharp volume bounds for a family of closed geodesics complements. The bounds depend only on the distance in the Farey graph.

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José Andrés Rodríguez Migueles. 2024-12-05. Geometry and topology of closed geodesics complements in the 3-torus. https://arxiv.org/abs/2412.03838

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