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Titlebook: Computational Homology; Tomasz Kaczynski,Konstantin Mischaikow,Marian Mroz Textbook 2004 Springer Science+Business Media New York 2004 Alg

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發(fā)表于 2025-3-21 19:41:57 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
書(shū)目名稱(chēng)Computational Homology
編輯Tomasz Kaczynski,Konstantin Mischaikow,Marian Mroz
視頻videohttp://file.papertrans.cn/233/232346/232346.mp4
概述This book by three experts takes a novel combinatorial computational approach to the subject of homology.It is the first book of its kind to appear.Includes supplementary material:
叢書(shū)名稱(chēng)Applied Mathematical Sciences
圖書(shū)封面Titlebook: Computational Homology;  Tomasz Kaczynski,Konstantin Mischaikow,Marian Mroz Textbook 2004 Springer Science+Business Media New York 2004 Alg
描述.Homology is a powerful tool used by mathematicians to study the properties of spaces and maps that are insensitive to small perturbations. This book uses a computer to develop a combinatorial computational approach to the subject.?The core of the book deals with homology theory and its computation. Following this is a section containing extensions to further developments in algebraic topology, applications to?computational dynamics, and applications to image processing. Included are exercises and software that can be used to compute homology groups and maps. The book will appeal to researchers and graduate students in mathematics, computer science, engineering, and nonlinear dynamics..
出版日期Textbook 2004
關(guān)鍵詞Algebraic topology; Homotopy; Lefschetz fixed-point theorem; algorithms; fixed-point theorem; homological
版次1
doihttps://doi.org/10.1007/b97315
isbn_softcover978-1-4419-2354-7
isbn_ebook978-0-387-21597-6Series ISSN 0066-5452 Series E-ISSN 2196-968X
issn_series 0066-5452
copyrightSpringer Science+Business Media New York 2004
The information of publication is updating

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Cubical Homologyimensional cubes). Before that we motivated the need for a computational theory of homology using examples from image processing where it was natural to think of the images as being presented in terms of pixels (two-dimensional cubes), voxels (three-dimensional cubes), and even tetrapus (four-dimens
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Computing Homology Groupsd .(.) for some simple examples and discussed the method of elementary collapse, which can be used in special cases to compute these groups. In this chapter we want to go further and argue that the homology groups of any cubical set are computable. In fact, we will derive Algorithm 3.78, which, give
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Preview of Mapss map .: . → .. It is natural to ask if . induces a group homomorphism .: .(.) → .(.). If so, do we get useful information out of it? The answer is yes and we will spend the next three chapters explaining how to define and compute .. It is worth noting, even at this very preliminary stage, that sinc
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Homology of Topological Polyhedraand 10, where we are required to work with large sets of data and for which we need a computationally effective means of computing homology. In all these examples the data itself naturally generates cubical sets. However, this cubical homology theory is unconventional, and furthermore, there is a wi
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