Topology for Computing

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Paperback | 8 November 2010

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260 Pages

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22.86 x 15.24 x 1.5

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The emerging field of computational topology utilizes theory from topology and the power of computing to solve problems in diverse fields. Recent applications include computer graphics, computer-aided design (CAD), and structural biology, all of which involve understanding the intrinsic shape of some real or abstract space. A primary goal of this book is to present basic concepts from topology and Morse theory to enable a non-specialist to grasp and participate in current research in computational topology. The author gives a self-contained presentation of the mathematical concepts from a computer scientist's point of view, combining point set topology, algebraic topology, group theory, differential manifolds, and Morse theory. He also presents some recent advances in the area, including topological persistence and hierarchical Morse complexes. Throughout, the focus is on computational challenges and on presenting algorithms and data structures when appropriate.

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'In my knowledge, it is the first book covering these topics.' Numerical Algorithms

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Introduction
Mathematics
Spaces and filtrations
Group theory
Homology
Morse theory
New results
Algorithms
The persistence algorithms
Topological simplification
The Morse-Smale algorithm
The linking number algorithm
Applications
Software
Experiments
Applications
Table of Contents provided by Publisher. All Rights Reserved.

Topology for Computing

At a Glance

Paperback

Industry Reviews

Shipping

How to return your order

Defective items

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Other Editions and Formats

Hardcover

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Mapping Analytic Surgery to Homology, Higher Rho Numbers and Metrics ofPositive Scalar Curvature

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