Description

Book Synopsis
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.

Table of Contents
  • A 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.

    Topological Persistence in Geometry and Analysis

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      £43.16

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      RRP £47.95 – you save £4.79 (9%)

      Order before 4pm today for delivery by Fri 7 Aug 2026.

      A Paperback by Leonid Polterovich, Daniel Rosen, Karina Samvelyan

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        Publisher: MP-AMM American Mathematical
        Publication Date: Publication Date: 6/30/2020 12:00:00 AM
        ISBN13: 9781470454951, 978-1470454951
        ISBN10: 1470454955

        Description

        Book Synopsis
        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.

        Table of Contents
        • A 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.

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