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arXiv · 2008.08494

Oblivious points on translation surfaces

Ian Adelstein·Krish Desai·Anthony Ji·Grace Zdeblick
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Abstract

An oblivious point on a translation surface is a point with no closed geodesic passing through it. Nguyen, Pan, and Su (2017) showed that there are at most finitely many oblivious points on any given translation surface and constructed a family of surfaces with exactly one oblivious point. We construct new families of translation surfaces with arbitrarily many oblivious points and prove that there is a translation surface in every genus $\ge3$ with an oblivious point.

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Ian Adelstein, Krish Desai, Anthony Ji, Grace Zdeblick. 2020-08-19. Oblivious points on translation surfaces. https://doi.org/10.1007/s00022-021-00620-4

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