When Left and Right Turns Inside Out: A Geometric and Categorical Introduction to an Inverse Problem in Persistence
Algebraic Topology
2019-02-27 v3
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.
Cite
@article{arxiv.1811.12392,
title = {When Left and Right Turns Inside Out: A Geometric and Categorical Introduction to an Inverse Problem in Persistence},
author = {Justin Curry},
journal= {arXiv preprint arXiv:1811.12392},
year = {2019}
}
Comments
This paper is being incorporated into future work