Discrete Morse theory
著者
書誌事項
Discrete Morse theory
（Student mathematical library, v. 90）
American Mathematical Society, c2019
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注記
Includes bibliographical references (p. 257-264) and indexes
内容説明・目次
内容説明
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. Its applications are vast, including applications to topological data analysis, combinatorics, and computer science.
This book, the first one devoted solely to discrete Morse theory, serves as an introduction to the subject. Since the book restricts the study of discrete Morse theory to abstract simplicial complexes, a course in mathematical proof writing is the only prerequisite needed. Topics covered include simplicial complexes, simple homotopy, collapsibility, gradient vector fields, Hasse diagrams, simplicial homology, persistent homology, discrete Morse inequalities, the Morse complex, discrete Morse homology, and strong discrete Morse functions. Students of computer science will also find the book beneficial as it includes topics such as Boolean functions, evasiveness, and has a chapter devoted to some computational aspects of discrete Morse theory. The book is appropriate for a course in discrete Morse theory, a supplemental text to a course in algebraic topology or topological combinatorics, or an independent study.
目次
What is discrete Morse theory?
Simplicial complexes
Discrete Morse theory
Simplicial homology
Main theorems of discrete Morse theory
Discrete Morse theory and persistent homology
Boolean functions and evasiveness
The Morse complex
Morse homology
Computations with discrete Morse theory
Strong discrete Morse theory
Bibliography
Notation and symbol index
Index.
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