Preface
A Computational Geometric Topology
I Graphs
I.1 Connected Components
I.2 Curves in the Plane
I.3 Knots and Links
I.4 Planar Graphs
Exercises

II Surfaces
II.1 2-dimensionalManifolds
II.2 Searching a Triangulation
II.3 Self-intersections
II.4 Surface Simplification
Exercises

III Complexes
III.1 Simplicial Complexes
III.2 Convex Set Systems
III.3 Delaunay Complexes
III.4 Alpha Complexes
Exercises

B Computational Algebraic Topology
IV Homology
IV.1 Homology Groups
IV.2 Matrix Reduction
IV.3 Relative Homology
IV.4 Exact Sequences
Exercises

V Duality
V.1 Cohomology
V.2 Poincar´e Duality
V.3 Intersection Theory
V.4 Alexander Duality
Exercises

VI Morse Functions
VI.1 Generic Smooth Functions
VI.2 Transversality
VI.3 Piecewise Linear Functions
VI.4 Reeb Graphs
Exercises

C Computational Persistent Topology
VII Persistence
VII.1 Persistent Homology
VII.2 Efficient Implementations
VII.3 Extended Persistence
VII.4 Spectral Sequences
Exercises

VIII Stability
VIII.1 1-parameter Families
VIII.2 Stability Theorems
VIII.3 Length of a Curve
VIII.4 Bipartite GraphMatching
Exercises

IX Applications
IX.1 Measures for Gene Expression Data
IX.2 Elevation for Protein Docking
IX.3 Persistence for Image Segmentation
IX.4 Homology for Root Architectures
Exercises

References
Index