Topology for Computing

This book presents basic concepts from the emerging field of computational topology, now being used to solve problems in diverse fields.

Afra J. Zomorodian (Author)

9780521136099, Cambridge University Press

Paperback, published 28 September 2009

260 pages, 118 b/w illus. 2 colour illus.
22.6 x 15.2 x 1.5 cm, 0.36 kg

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

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.

1. Introduction
Part I. Mathematics: 2. Spaces and filtrations
3. Group theory
4. Homology
5. Morse theory
6. New results
Part II. Algorithms: 7. The persistence algorithms
8. Topological simplification
9. The Morse–Smale algorithm
10. The linking number algorithm
Part III. Applications: 11. Software
12. Experiments
13. Applications.

Subject Areas: Mathematical theory of computation [UYA], Topology [PBP]