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.^[1]
Discrete Morse theory is a combinatorial adaptation of Morse theory developed by Robin Forman.^[2]
Discrete Morse theory is a powerful tool combining ideas in both topology and combinatorics.^[3]
Invented by Robin Forman in the mid 1990s, discrete Morse theory is a combinatorial analogue of Marston Morse's classical Morse theory.^[3]
Discrete Morse Theory is the study of discrete topological spaces from the perspective of certain functions defined on such spaces.^[4]
In this book, Nicholas Scoville provides an extremely accessible introduction to discrete Morse theory, aimed at an undergraduate audience.^[4]
Scoville introduces persistent homology in Chapter 5, which connects discrete Morse theory to topological data analysis.^[4]
Discrete Morse theory was developed by Forman as a combinatorial analog to the classical smooth Morse theory.^[5]