Topology for Computing

Afra J. Zomorodian - Collection Cambridge Monographs on Applied and Computational Mahematics

264 pages, parution le 02/03/2005

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Résumé

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.

L'auteur - Afra J. Zomorodian

Afra J. Zomorodian: Stanford University, California

Sommaire

Part I. Mathematics
- Spaces and filtrations
- Group theory
- Homology
- Morse theory
- New results
Part II Algorithms
- The persistence algorithms
- Topological simplification
- The Morse-Smale algorithm
- The linking number algorithm
Part III Applications
- Software
- Experiments
- Applications

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	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	Afra J. Zomorodian
Collection	Cambridge Monographs on Applied and Computational Mahematics
Parution	02/03/2005
Nb. de pages	264
Format	15,5 x 23,5
Couverture	Relié
Poids	465g
Intérieur	Noir et Blanc
EAN13	9780521836661
ISBN13	978-0-521-83666-1