Graphs, Surfaces and Homology, Giblin

Автор: Kaczynski
Название: Computational Homology
ISBN: 0387408533 ISBN-13(EAN): 9780387408538
Издательство: Springer
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Цена: 13974.00 р.
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Описание: Uses the computer to take a combinatorial computational approach to homological problems. This interdisciplinary book is aimed at researchers and students in mathematics, computer science, nonlinear dynamics, and engineering.

Автор: Tomasz Kaczynski, Konstantin Mischaikow, Marian Mr
Название: Computational Homology
ISBN: 1441923543 ISBN-13(EAN): 9781441923547
Издательство: Springer
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Цена: 10480.00 р.
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Описание: Homology is a powerful tool used by mathematicians to study the properties of spaces and maps that are insensitive to small perturbations. Following this is a section containing extensions to further developments in algebraic topology, applications to computational dynamics, and applications to image processing.

Автор: Banyaga Augustin, Hurtubise David
Название: Lectures on Morse Homology
ISBN: 1402026951 ISBN-13(EAN): 9781402026959
Издательство: Springer
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Цена: 11179.00 р.
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Описание: This book presents in great detail all the results one needs to prove the Morse Homology Theorem using classical techniques from algebraic topology and homotopy theory. Most of these results can be found scattered throughout the literature dating from the mid to late 1900's in some form or other, but often the results are proved in different contexts with a multitude of different notations and different goals. This book collects all these results together into a single reference with complete and detailed proofs.The core material in this book includes CW-complexes, Morse theory, hyperbolic dynamical systems (the Lamba-Lemma, the Stable/Unstable Manifold Theorem), transversality theory, the Morse-Smale-Witten boundary operator, and Conley index theory. More advanced topics include Morse theory on Grassmann manifolds and Lie groups, and an overview of Floer homology theories. With the stress on completeness and by its elementary approach to Morse homology, this book is suitable as a textbook for a graduate level course, or as a reference for working mathematicians and physicists.