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Topological persistence in geometry and analysis. (English) Zbl 07275267
University Lecture Series 74. Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-5495-1/pbk; 978-1-4704-5679-5/ebook). xi, 128 p. (2020).
Preliminary review / Publisher’s description: he 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.
55-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic topology
55-02 Research exposition (monographs, survey articles) pertaining to algebraic topology
55N31 Persistent homology and applications, topological data analysis
58Cxx Calculus on manifolds; nonlinear operators
53Dxx Symplectic geometry, contact geometry