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arXiv · 1711.10757

A lower bound for the volumes of complements of periodic geodesics

José Andrés Rodríguez Migueles
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Abstract

Every closed geodesic $\gamma$ on a surface has a canonically associated knot $\widehat\gamma$ in the projective unit tangent bundle. We study, for $\gamma$ filling, the volume of the associated knot complement with respect to its unique complete hyperbolic metric. We provide a lower bound for the volume relative to the number of homotopy classes of $\gamma$-arcs in each pair of pants of a pants decomposition of the surface.

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José Andrés Rodríguez Migueles. 2017-11-29. A lower bound for the volumes of complements of periodic geodesics. https://doi.org/10.1112/jlms.12333

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