Topological Persistence In Geometry And Analysis
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Topological Persistence in Geometry and Analysis
Author: Leonid Polterovich
language: en
Publisher: American Mathematical Soc.
Release Date: 2020-05-11
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.
Computational Topology for Data Analysis
Author: Tamal Krishna Dey
language: en
Publisher: Cambridge University Press
Release Date: 2022-03-10
This book provides a computational and algorithmic foundation for techniques in topological data analysis, with examples and exercises.
Geometric and Topological Inference
Author: Jean-Daniel Boissonnat
language: en
Publisher: Cambridge University Press
Release Date: 2018-09-27
A rigorous introduction to geometric and topological inference, for anyone interested in a geometric approach to data science.