Kaczynski / Mischaikow / Mrozek Computational Homology

Erscheinungsjahr 2006
ISBN: 978-0-387-21597-6
Verlag: Springer US
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 157, 482 Seiten, eBook

Reihe: Applied Mathematical Sciences

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.

Zielgruppe

Graduate

Autoren/Hrsg.

Kaczynski, Tomasz

Mischaikow, Konstantin

Mrozek, Marian

Inhaltsverzeichnis

Homology.- Preview.- Cubical Homology.- Computing Homology Groups.- Chain Maps and Reduction Algorithms.- Preview of Maps.- Homology of Maps.- Computing Homology of Maps.- Extensions.- Prospects in Digital Image Processing.- Homological Algebra.- Nonlinear Dynamics.- Homology of Topological Polyhedra.- Tools from Topology and Algebra.- Topology.- Algebra.- Syntax of Algorithms.