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OverviewThe 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. Full Product DetailsAuthor: Leonid Polterovich , Daniel Rosen , Karina Samvelyan , Jun ZhangPublisher: American Mathematical Society Imprint: American Mathematical Society Weight: 0.265kg ISBN: 9781470454951ISBN 10: 1470454955 Pages: 140 Publication Date: 30 June 2020 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsA primer of persistence modules: Definition and first examples Barcodes Proof of the isometry theorem What can we read from a barcode? Applications to metric geometry and function theory: Applications of Rips complexes Topological function theory Persistent homology in symplectic geometry: A concise introduction to symplectic geometry Hamiltonian persistence modules Symplectic persistence modules Bibliography Notation index Subject index Name index.ReviewsAuthor InformationLeonid Polterovich, Tel Aviv University, Israel. Daniel Rosen, Ruhr-Universitat Bochum, Germany. Karina Samvelyan, Tel Aviv University, Israel. Jun Zhang, Universite de Montreal, Canada. Tab Content 6Author Website:Countries AvailableAll regions |
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