Topological persistence in geometry and analysis
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. …
Read More ↓Title Statements
- Full title :Topological persistence in geometry and analysis / Leonid Polterovich, Daniel Rosen, Karina Samvelyan, Jun Zhang.
Summary
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.
Read More ↓Edition Statements
- Publication Date:©2020
Publication Statements
- Publisher(s):American mathematical Society
- Place of Publication:Providence, Rhode Island
- Language:eng
- Publication Date:©2020
The Physical Object
- Description:1 online resource (xi, 128 pages) : : illustrations
Edition Identifiers
- ISBN:9781470456795, 1470456796
- oclc:on1159168787
- LC Classification:QA612
- Dewey Decimal:514/.2
Table of Contents
Definition and first examples -- Barcodes -- Proof of the isometry theorem -- What can we read from a barcode? -- Applications of Rips complexes -- Topological function theory -- A concise introduction to symplectic geometry -- Hamiltonian persistence modules -- Symplectic persistence modules.
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