Discrete Morse Theory

Discrete Morse Theory
Author :
Publisher : American Mathematical Soc.
Total Pages : 289
Release :
ISBN-10 : 9781470452988
ISBN-13 : 1470452987
Rating : 4/5 (987 Downloads)

Book Synopsis Discrete Morse Theory by : Nicholas A. Scoville

Download or read book Discrete Morse Theory written by Nicholas A. Scoville and published by American Mathematical Soc.. This book was released on 2019-09-27 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.


Discrete Morse Theory Related Books

Discrete Morse Theory
Language: en
Pages: 289
Authors: Nicholas A. Scoville
Categories: Mathematics
Type: BOOK - Published: 2019-09-27 - Publisher: American Mathematical Soc.

GET EBOOK

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
Organized Collapse: An Introduction to Discrete Morse Theory
Language: en
Pages: 312
Authors: Dmitry N. Kozlov
Categories: Mathematics
Type: BOOK - Published: 2021-02-18 - Publisher: American Mathematical Society

GET EBOOK

Applied topology is a modern subject which emerged in recent years at a crossroads of many methods, all of them topological in nature, which were used in a wide
Morse Theory: Smooth And Discrete
Language: en
Pages: 196
Authors: Kevin P Knudson
Categories: Mathematics
Type: BOOK - Published: 2015-05-29 - Publisher: World Scientific Publishing Company

GET EBOOK

Morse Theory: Smooth and Discrete serves as an introduction to classical smooth Morse theory and to Forman's discrete Morse theory, highlighting the parallels b
An Introduction to Morse Theory
Language: en
Pages: 244
Authors: Yukio Matsumoto
Categories: Mathematics
Type: BOOK - Published: 2002 - Publisher: American Mathematical Soc.

GET EBOOK

Finite-dimensional Morse theory is easier to present fundamental ideas than in infinite-dimensional Morse theory, which is theoretically more involved. However,
An Invitation to Morse Theory
Language: en
Pages: 366
Authors: Liviu Nicolaescu
Categories: Mathematics
Type: BOOK - Published: 2011-12-02 - Publisher: Springer Science & Business Media

GET EBOOK

This self-contained treatment of Morse theory focuses on applications and is intended for a graduate course on differential or algebraic topology, and will also