Topological Persistence in Geometry and Analysis

Download or read book Topological Persistence in Geometry and Analysis written by Leonid Polterovich and published by American Mathematical Soc.. This book was released on 2020-05-11 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of persistence modules originated in topological data analysis and became an active area of research in algebraic topology. This book provides a concise and self-contained introduction to persistence modules and focuses on their interactions with pure mathematics, bringing the reader to the cutting edge of current research. In particular, the authors present applications of persistence to symplectic topology, including the geometry of symplectomorphism groups and embedding problems. Furthermore, they discuss topological function theory, which provides new insight into oscillation of functions. The book is accessible to readers with a basic background in algebraic and differential topology.