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arXiv · 1811.12392

When Left and Right Turns Inside Out: A Geometric and Categorical Introduction to an Inverse Problem in Persistence

Justin Curry
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Abstract

In this paper we introduce the problem of counting embedded spheres in R^3 whose projection to the z-axis yields a level set barcode of a particular type. Two embedded spheres are considered height equivalent if they are related by a z-level set preserving isotopy. A formula previously used to count functions on the interval with the same sub-level set persistence barcode provides a lower bound on height equivalence classes with the same level set persistence. A conjectured upper bound is provided as well.

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Justin Curry. 2018-11-29. When Left and Right Turns Inside Out: A Geometric and Categorical Introduction to an Inverse Problem in Persistence. https://arxiv.org/abs/1811.12392

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