Computational topology

Algorithmic topology, or computational topology, is a subfield of topology with an overlap with areas of computer science, in particular computational geometry and computational complexity theory.

A primary concern of algorithmic topology, as its name suggests, is to develop efficient algorithms for solving topological problems. For example, an open problem, called the unknotting problem, is to find a polynomial time algorithm to see if a knot is unknotted.

Some parts of algorithmic topology can be considered experimental mathematics.

A major new area of computational topology is topological data analysis.

External links

• CompuTop software archive
• Workshop on Application of Topology in Science and Engineering

Books

• Tomasz Kaczynski, Konstantin Mischaikow, Marian Mrozek (2004). Computational Homology. Springer. ISBN 0-387-40853-3. 
• Afra J. Zomorodian (2005). Topology for Computing. Cambridge. ISBN 0-521-83666-2.