Softcover ISBN:  9781470454951 
Product Code:  ULECT/74 
List Price:  $55.00 
MAA Member Price:  $49.50 
AMS Member Price:  $44.00 
eBook ISBN:  9781470456795 
Product Code:  ULECT/74.E 
List Price:  $55.00 
MAA Member Price:  $49.50 
AMS Member Price:  $44.00 
Softcover ISBN:  9781470454951 
eBook: ISBN:  9781470456795 
Product Code:  ULECT/74.B 
List Price:  $110.00 $82.50 
MAA Member Price:  $99.00 $74.25 
AMS Member Price:  $88.00 $66.00 
Softcover ISBN:  9781470454951 
Product Code:  ULECT/74 
List Price:  $55.00 
MAA Member Price:  $49.50 
AMS Member Price:  $44.00 
eBook ISBN:  9781470456795 
Product Code:  ULECT/74.E 
List Price:  $55.00 
MAA Member Price:  $49.50 
AMS Member Price:  $44.00 
Softcover ISBN:  9781470454951 
eBook ISBN:  9781470456795 
Product Code:  ULECT/74.B 
List Price:  $110.00 $82.50 
MAA Member Price:  $99.00 $74.25 
AMS Member Price:  $88.00 $66.00 

Book DetailsUniversity Lecture SeriesVolume: 74; 2020; 128 ppMSC: Primary 55; 58; 53
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 selfcontained 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.
ReadershipGraduate students and researchers interested in applications of new methods of computational topology to function theory and symplectic geometry.

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


Additional Material

Reviews

One nice feature of this short book is that it is interactive in the sense that there are exercises for the reader to work on interspersed throughout the text. The exercises, of course, vary in difficulty. Another feature is that in addition to a subject index, there is both a notational index as well as a name index. It provides a good introduction to anyone wishing to learn about the subject and a reference for practitioners of the subject.
Nick Scoville, Ursinus College, MAA Reviews


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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 selfcontained 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.
Graduate students and researchers interested in applications of new methods of computational topology to function theory and symplectic geometry.

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

One nice feature of this short book is that it is interactive in the sense that there are exercises for the reader to work on interspersed throughout the text. The exercises, of course, vary in difficulty. Another feature is that in addition to a subject index, there is both a notational index as well as a name index. It provides a good introduction to anyone wishing to learn about the subject and a reference for practitioners of the subject.
Nick Scoville, Ursinus College, MAA Reviews