Organized collapse: an introduction to discrete Morse theory
by Kozlov, D. N., (Dmitriĭ Nikolaevich)
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 variety of applications in classical mathematics and beyond. Within applied topology, discrete Morse theory came into light as one of the main tools to understand cell complexes arising in different contexts, as well as to reduce the complexity of homology calculations. The present book provides a gentle introduction into this beautiful…
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- Full title :Organized collapse : an introduction to discrete Morse theory / Dmitry N. Kozlov.
Summary
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 variety of applications in classical mathematics and beyond. Within applied topology, discrete Morse theory came into light as one of the main tools to understand cell complexes arising in different contexts, as well as to reduce the complexity of homology calculations. The present book provides a gentle introduction into this beautiful theory. Using a combinatorial approach--the author emphasizes acyclic matchings as the central object.
Read More ↓Edition Statements
- Publication Date:©2020
Publication Statements
- Publisher(s):American mathematical Society
- Place of Publication:Providence, Rhode Island
- Language:eng
- Publication Date:©2020
The Physical Object
- Description:1 online resource (xxiii, 312 pages) : : illustrations.
Edition Identifiers
- ISBN:9781470460082, 1470460084
- oclc:on1164504927
- LC Classification:QA612.14
- Dewey Decimal:514/.2
Table of Contents
The first steps -- Simplicial homology -- Beyond the simplicial setting -- Category of chain complexes -- Chain homotopy -- Connecting homomorphism -- Singular homology -- Cellular homology -- Simplicial collapses -- Organizing collapsing sequences -- Internal collapses and discrete Morse theory -- Explicit homology classes associated to critical cells -- The critical Morse complex -- Implications and variations -- Algebraic Morse theory -- Discrete Morse theory for posets -- Discrete Morse theory for CW complexes -- Discrete Morse theory and persistence.
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