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" Discrete Morse theory / "
Nicholas A. Scoville.
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BL
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| Record Number
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850333
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| Main Entry
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Scoville, Nicholas A.
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| Title & Author
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Discrete Morse theory /\ Nicholas A. Scoville.
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| Publication Statement
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Providence, Rhode Island :: American Mathematical Society,, [2019]
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| Series Statement
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Student mathematical library ;; volume 90
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| Page. NO
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xiv, 273 pages :: illustrations ;; 22 cm.
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| ISBN
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1470452987
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: 9781470452988
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9781470453794
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| Bibliographies/Indexes
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Includes bibliographical references (pages 257-264) and index.
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| Contents
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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.
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| Abstract
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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.
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| Subject
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Geometry, Differential.
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Homotopy theory.
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Morse theory.
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Algebraic topology -- Applied homological algebra and category theory [See also 18Gxx] -- Abstract complexes.
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Geometry, Differential.
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Global analysis, analysis on manifolds [See also 32Cxx, 32Fxx, 32Wxx, 46-XX, 47Hxx, 53Cxx] {For geometric integration theory, see 49Q15} -- Variational problems in infinite-dimensional spaces -- Abstr.
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Homotopy theory.
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Manifolds and cell complexes {For complex manifolds, see 32Qxx} -- PL-topology -- General topology of complexes.
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Manifolds and cell complexes {For complex manifolds, see 32Qxx} -- PL-topology -- Simple homotopy type, Whitehead torsion, Reidemeister-Franz torsion, etc. [See also 19B28].
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| Subject
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Morse theory.
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| Subject
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Morse-Theorie
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| Dewey Classification
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514.24
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| LC Classification
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QA612.7.S36 2019
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| NLM classification
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55U0558E0557Q0557Q10msc
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