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.
Table of Contents
* Cubical Homology
* Computing Homology Groups
* Chain Maps and Reduction Algorithms
* Preview of Maps
* Homology of Maps
* Computing Homology of Maps
* Prospects in Digital Image Processing
* Homological Algebra
* Nonlinear Dynamics
* Homology of Topological Polyhedra
* Topology * Algebra
* Syntax of Algorithms
* References * Symbol Index * Subject Index.