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  3. Topology for Computing
  • Cited by 155
Publisher:
Cambridge University Press
Online publication date:
August 2009
Print publication year:
2005
Online ISBN:
9780511546945
DOI:
https://doi.org/10.1017/CBO9780511546945
Subjects:
Mathematics, Computational Science, Computer Science, Computer Graphics, Image Processing and Robotics, Geometry and Topology
Series:
Cambridge Monographs on Applied and Computational Mathematics (16)
Information

Book description

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.

Reviews

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

Source: Numerical Algorithms

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