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.

About the Author

Leonid Polterovich, Tel Aviv University, Israel.

Daniel Rosen, Ruhr-Universitat Bochum, Germany.

Karina Samvelyan, Tel Aviv University, Israel.

Jun Zhang, Universite de Montreal, Canada.