Topological Persistence in Geometry and Analysis
Algebraic Topology
2021-01-26 v2 Classical Analysis and ODEs
Symplectic Geometry
Abstract
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.
Cite
@article{arxiv.1904.04044,
title = {Topological Persistence in Geometry and Analysis},
author = {Leonid Polterovich and Daniel Rosen and Karina Samvelyan and Jun Zhang},
journal= {arXiv preprint arXiv:1904.04044},
year = {2021}
}
Comments
An Erratum added