Topology for Computing by Zomorodian

Topology for Computing by Afra Zomorodian is an early book in computational topology.

The book is a research monograph based on the author's PhD thesis in applied mathematics. It that provides both mathematical foundation and the algorithms for computation of topological features, i.e., homology, of geometric objects. The methods apply only to simplicial complexes. This is sufficient to cover point clouds and topological data analysis but not digital images.

Contents

• Part I: Mathematics
  • Spaces and Filtrations
  • Group Theory
  • Homology
  • Morse Theory
  • New Results
• Part II: Algorithms
  • The Persistence Algorithms
  • Topological Simplification
  • The Morse-Smale Complex Algorithm
  • The Linking Number Algorithm
• Part III: Applications
  • Software
  • Experiments
  • Applications