2019/04/30 by Leonid Polterovich, Daniel Rosen, Karina Samvelyan +1 · 3 citations
Mathematics · #math.AT #math.CA #math.SG #msc:55U99 #msc:58Cxx #msc:53Dxx
published as University Lecture Series, 74. American Mathematical Society, Providence, RI, 2020. 128 pp. ISBN:978-1-4704-5495-1 · An Erratum added
arxiv created 2021/01/23 · arxiv updated 2021/01/26
The theory of persistence modules is an emerging field of algebraic topology which originated in topological data analysis. In these notes we provide a concise introduction into this field and give an account on some of its interactions with geometry and analysis. In particular, we present applications of persistence to symplectic topology, including the geometry of symplectomorphism groups and embedding problems. Furthermore, we discuss topological function theory which provides a new insight on oscillation of functions. The material should be accessible to readers with a basic background in algebraic and differential topology.