English

Oblivious points on translation surfaces

Geometric Topology 2022-01-11 v2 Differential Geometry

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 3\ge3 with an oblivious point.

Cite

@article{arxiv.2008.08494,
  title  = {Oblivious points on translation surfaces},
  author = {Ian Adelstein and Krish Desai and Anthony Ji and Grace Zdeblick},
  journal= {arXiv preprint arXiv:2008.08494},
  year   = {2022}
}

Comments

This version has been revised for publication

R2 v1 2026-06-23T17:57:57.247Z