Articoli correlati a Topological Persistence in Geometry and Analysis

Topological Persistence in Geometry and Analysis - Brossura

Polterovich, Leonid; Rosen, Daniel; Samvelyan, Karina; Zhang, Jun

 
9781470454951: Topological Persistence in Geometry and Analysis

Sinossi

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.

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