Topological Persistence in Geometry and Analysis

Leonid Polterovich; Daniel Rosen; Karina Samvelyan; Jun Zhang

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arXiv · 1904.04044

Topological Persistence in Geometry and Analysis

Leonid Polterovich·Daniel Rosen·Karina Samvelyan·Jun Zhang

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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.

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BibTeX RIS

Leonid Polterovich, Daniel Rosen, Karina Samvelyan, Jun Zhang. 2019-04-08. Topological Persistence in Geometry and Analysis. https://arxiv.org/abs/1904.04044

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