Topology for computing

Zomorodian A.J.0511082207

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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Table of contents :
Cover Page……Page 1
CAMBRIDGE MONOGRAPH – Topology for Computing……Page 3
Title Page……Page 5
Edition Info……Page 6
Contents……Page 9
Preface……Page 13
Acknowledgments……Page 15
1 Introduction……Page 17
Part One: Mathematics……Page 27
2 Spaces and Filtrations……Page 29
3 Group Theory……Page 57
4 Homology……Page 76
5 Morse Theory……Page 99
6 New Results……Page 110
Part Two: Algorithms……Page 139
7 The Persistence Algorithms……Page 141
8 Topological Simplification……Page 164
9 The Morse-Smale Complex Algorithm……Page 177
10 The Linking Number Algorithm……Page 187
Part Three: Applications……Page 197
11 Software……Page 199
12 Experiments……Page 214
13 Applications……Page 239
Bibliography……Page 251
Index……Page 256