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# Computational Topology by Edelsbrunner and Harer

### From Mathematics Is A Science

Contents

Part a

- Surfaces 27
- Searching a triangulation 33
- Selfintersections 37
- Surface simplification 42

- Complexes 51
- Convex set systems 57
- Delaunay complexes 63
- Alpha complexes 68

Part b: Computational algebraic topology 77

- Homology 79

- Duality 103
- Poincare duality 108
- Intersection theory 114
- Alexander duality 118

- Morse functions 125
- Transversality 130
- Piecewise linear functions 135
- Reeb graphs 140

Part b: Computational persistent topology 147

- Persistence 149
- Efficient implementations 156
- Extended persistence 161
- Spectral sequences 166

- Stability 175
- Stability theorems 180
- lengths of curves 185
- Bipartite graph matching 191

- Applications 199
- Elevation for protein docking 206
- Persistence for image segmentation 213
- Homology for root architectures 218