Abstract
An oblivious point on a translation surface is a point with no closed geodesic passing through it. Nguyen et al. (Mathematische Annalen, 2017, https://doi.org/10.1007/s00208-019-01897-2) 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 \(\ge 3\) with an oblivious point.
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