Discrete Morse theory

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• Here, we refine the study of the complexity of problems related to discrete Morse theory in terms of parameterized complexity.
• Discrete Morse theory is a combinatorial adaptation of Morse theory developed by Robin Forman.
• Discrete Morse theory is a powerful tool combining ideas in both topology and combinatorics.
• Invented by Robin Forman in the mid 1990s, discrete Morse theory is a combinatorial analogue of Marston Morse's classical Morse theory.
• Discrete Morse Theory is the study of discrete topological spaces from the perspective of certain functions defined on such spaces.
• In this book, Nicholas Scoville provides an extremely accessible introduction to discrete Morse theory, aimed at an undergraduate audience.
• Scoville introduces persistent homology in Chapter 5, which connects discrete Morse theory to topological data analysis.
• Discrete Morse theory was developed by Forman as a combinatorial analog to the classical smooth Morse theory.