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Computational topology is the study of decidability problems in topology and the algorithms that determine decidability. Examples of area of study include Normal Surface theory and the subproblems of unknot and $S^3$ recognition.
11
votes
Computer-aided homology computations
There are several applications and libraries out there that deal with homology computations with various approaches to the computation. One field with a strong focus on efficient computation of homolo …
8
votes
Persistent homology of Gaussian fields in Euclidean space
The closest I can find spontaneously would be Matthew Kahle's work on random topology; http://arxiv.org/abs/0910.1649 looks like it would be directly related to your question, and http://arxiv.org/abs …