Computational Topology

Question

So I've revently gotten an opportunity to begin independent study in a field of my interest. As it turns out a close friend of mine is a post doctoral researcher who's working on essentially topological analysis of a fluid dynamics experiment. I'm looking for a book or series of books which would provide a good introduction to both fluid dynamics and computational topology. If anyone has any suggestions that would be great! Thanks.

Answer 1

I don't know whether they discuss fluid dynamics, but try these books:

• Computational Topology: An Introduction by Edelsbrunner and Harer.

• Topology for Computing by Zomorodian.

There is also this paper:

• Computational Topology: An Introduction by Rote and Vegter.

Answer 2

I can't say much about fluid dynamics, but on the computational topology side of things, one research push in low-dimensional topology right now is effective geometrization, the computational study of geometry and topology. There are lots of existence theorems, but can we realize or approximate those results constructively with relatively efficient numerical algorithms?

Nathan Dunfield, at the University of Illinois Urbana-Champaign, maintains CompuTop, a website that archives various software packages that have been written in pursuit of numerical study of topological and geometric problems.