Discrete Morse theory:
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 d...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, Rhode Island
American Mathematical Society
[2019]
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| Schriftenreihe: | Student mathematical library
Volume 90 |
| Schlagworte: | |
| Zusammenfassung: | 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 |
| Beschreibung: | xiv, 273 Seiten Illustrationen 22 cm |
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| 505 | 8 | |a 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 | |
| 520 | |a 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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Datensatz im Suchindex
| _version_ | 1804180767268405248 |
|---|---|
| any_adam_object | |
| author | Scoville, Nicholas A. |
| author_GND | (DE-588)1199301965 |
| author_facet | Scoville, Nicholas A. |
| author_role | aut |
| author_sort | Scoville, Nicholas A. |
| author_variant | n a s na nas |
| building | Verbundindex |
| bvnumber | BV046299094 |
| classification_rvk | SK 350 |
| contents | 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 |
| ctrlnum | (OCoLC)1131809363 (DE-599)BVBBV046299094 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV046299094 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T08:40:59Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-031676461 |
| oclc_num | 1131809363 |
| open_access_boolean | |
| owner | DE-20 DE-83 DE-188 |
| owner_facet | DE-20 DE-83 DE-188 |
| physical | xiv, 273 Seiten Illustrationen 22 cm |
| publishDate | 2019 |
| publishDateSearch | 2019 |
| publishDateSort | 2019 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Student mathematical library |
| series2 | Student mathematical library |
| spelling | Scoville, Nicholas A. (DE-588)1199301965 aut Discrete Morse theory Nicholas A. Scoville Providence, Rhode Island American Mathematical Society [2019] © 2019 xiv, 273 Seiten Illustrationen 22 cm txt rdacontent n rdamedia nc rdacarrier Student mathematical library Volume 90 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 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 Morse theory Homotopy theory Geometry, Differential Geometry, Differential fast Homotopy theory fast Morse theory fast Morse-Theorie (DE-588)4197103-6 gnd rswk-swf Morse-Theorie (DE-588)4197103-6 s DE-604 Student mathematical library Volume 90 (DE-604)BV013184751 90 |
| spellingShingle | Scoville, Nicholas A. Discrete Morse theory Student mathematical library 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 Morse theory Homotopy theory Geometry, Differential Geometry, Differential fast Homotopy theory fast Morse theory fast Morse-Theorie (DE-588)4197103-6 gnd |
| subject_GND | (DE-588)4197103-6 |
| title | Discrete Morse theory |
| title_auth | Discrete Morse theory |
| title_exact_search | Discrete Morse theory |
| title_full | Discrete Morse theory Nicholas A. Scoville |
| title_fullStr | Discrete Morse theory Nicholas A. Scoville |
| title_full_unstemmed | Discrete Morse theory Nicholas A. Scoville |
| title_short | Discrete Morse theory |
| title_sort | discrete morse theory |
| topic | Morse theory Homotopy theory Geometry, Differential Geometry, Differential fast Homotopy theory fast Morse theory fast Morse-Theorie (DE-588)4197103-6 gnd |
| topic_facet | Morse theory Homotopy theory Geometry, Differential Morse-Theorie |
| volume_link | (DE-604)BV013184751 |
| work_keys_str_mv | AT scovillenicholasa discretemorsetheory |