Topological persistence in geometry and analysis
著者
書誌事項
Topological persistence in geometry and analysis
（University lecture series, volume74）
American Mathematical Society, c2020
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注記
Includes bibliographical references (p. 115-119) and indexes
内容説明・目次
内容説明
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.
目次
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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