Computational Homology

• Main Authors: Kaczynski, Tomasz (Author), Mischaikow, Konstantin (Author), Mrozek, Marian (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: New York, NY : Springer New York : Imprint: Springer, 2004.
• Series: Applied Mathematical Sciences, 157
• Subjects: Mathematics.; Category theory (Mathematics).; Homological algebra.; Dynamics.; Ergodic theory.; Applied mathematics.; Engineering mathematics.; Computer mathematics.; Topology.; Algebraic topology.; Applications of Mathematics.; Category Theory, Homological Algebra.; Dynamical Systems and Ergodic Theory.; Computational Mathematics and Numerical Analysis.; Algebraic Topology.

In recent years, there has been a growing interest in applying homology to problems involving geometric data sets, whether obtained from physical measurements or generated through numerical simulations. This book presents a novel approach to homology that emphasizes the development of efficient algo...

Table of Contents:

• 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.