Description

Book Synopsis
Provides 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

Organized Collapse An Introduction to Discrete

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    A Paperback by Dmitry N. Kozlov

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      Publisher: MP-AMM American Mathematical
      Publication Date: 4/30/2021 12:00:00 AM
      ISBN13: 9781470464554, 978-1470464554
      ISBN10: 1470464551
      Also in:
      Algebra Topology

      Description

      Book Synopsis
      Provides 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

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