Morse Theory

Smooth and Discrete

Morse Theory: Smooth and Discrete serves as an introduction to classical smooth Morse theory and to Forman's discrete Morse theory, highlighting the parallels between the two subjects. This is the first time both smooth and discrete Morse theory have been treated in a single volume. This makes the book a valuable resource for students and professionals working in topology and discrete mathematics. With a strong focus on examples, the text is suitable for advanced undergraduates or beginning graduate students.

Contents:

• Smooth Morse Theory:

  • First Steps
  • Fundamental Results in Morse Theory
  • Topological Consequences
  • Homology
  • Piecewise Linear Morse Theory

• Discrete Morse Theory:

  • First Steps
  • Topological Consequences
  • Algorithms
  • Applications

• Appendices:

  • Smooth Manifolds
  • Cell Complexes

Readership: Graduate students in geometry and topology.
Key Features:

• It is the first time these topics have been treated in the same volume
• Accessible introduction to smooth Morse theory, aimed at students
• Text includes many worked examples