Inverse Problems in Topological Persistence: a Survey
Résumé
In this survey, we review the literature on inverse problems in topological persistence theory.The first half of the survey is concerned with the question of surjectivity, i.e. the existence of rightinverses, and the second half focuses on injectivity, i.e. left inverses. Throughout, we highlightthe tools and theorems that underlie these advances, and direct the reader’s attention to openproblems, both theoretical and applied.