Description
Book SynopsisProvides a gentle introduction into discrete Morse theory. Using a combinatorial approach, the author emphasizes acyclic matchings as the central object of study. The first two parts of the book can be used as a stand-alone introduction to homology, the last two parts delve into the core of discrete Morse theory.
Table of Contents
- Preamble
- Preface
- The idea of homology
- The idea of discrete Morse theory
- A sample application
- How to use this book
- Prerequisites
- Guide to the literature
- Part 1 . Introduction to Homology
- Chapter 1. The First Steps
- Chapter 2. Simplicial Homology
- Chapter 3. Beyond the Simplicial Setting
- Part 2 . Further Aspects of Homology Theory
- Chapter 4. Category of Chain Complexes
- Chapter 5. Chain Homotopy
- Chapter 6. Connecting Homomorphism
- Chapter 7. Singular Homology
- Chapter 8. Cellular Homology
- Suggested further reading for Parts 1 and 2
- Part 3 . Basic Discrete Morse Theory
- Chapter 9. Simplicial Collapses
- Chapter 10. Organizing Collapsing Sequences
- Chapter 11. Internal Collapses and Discrete Morse Theory
- Chapter 12. Explicit Homology Classes Associated to Critical Cells
- Chapter 13. The Critical Morse Complex
- Chapter 14. Implications and Variations
- Suggested further reading for Part 3
- Part 4 . Extensions of Discrete Morse Theory
- Chapter 15. Algebraic Morse Theory
- Chapter 16. Discrete Morse Theory for Posets
- Chapter 17. Discrete Morse Theory for CW Complexes
- Chapter 18. Discrete Morse Theory and Persistence
- Suggested further reading for Part 4
- Index
- List of Figures
- List of Tables
- Bibliography
- Index
- Preview Material
- Preface
- Table of Contents
