Introduction to Computational Topology

Question: Besides generally learning Algebraic Topology, what are some prerequisites for studying Computational Topology? Are there any accessible papers which introduce the field and the methods being used?

Motivation: A number of my peers do applied mathematics where I go to school, and upon hearing how they solved problems for their applied math classes I often think that the same sort of techniques could be used in topology. I am often referred to Stanford's computation topology page, though a number of the preprints on this page are not quite accessible to me. Of course, accessibility is subjective, but I wanted to see if anyone had any suggestions regarding how to proceed. It would be a shame to give up on this interesting looking subject just because I can't get my foot in the door!

• Upper management disabled the CW option for ordinary users; only moderators can enable it now (which I've just done). – Qiaochu Yuan Apr 2 '11 at 20:46
• Take a look at the Wikipedia page: en.wikipedia.org/wiki/Computational_topology in particular the Edelsbrunner & Harer book referenced. Your "motivation" section isn't clear to me. Could you clarify your 1st sentence from "Motivation"? What topology problems do you have in mind? Computational topology in the sense of the Stanford group is completely the opposite -- it's about using topology to solve practical problems, not about using "applied math" techniques to solve topology problems. – Ryan Budney Apr 2 '11 at 21:27
• The book of Matousek "Using the Borsuk-Ulam Theorem" is an excellent introduction to applications of topology to combinatorics and geometry. This a very young topic which is gaining a lot of interest and is definitively worth checking out. – David Kohler Apr 2 '11 at 23:09
• Okay. IMO the best way to get a sense for how you could apply algebraic topology would be to learn the basics of the subject first. This is a bit like asking how one could apply calculus to physics without first knowing any calculus. Would you like an explanation at that level of vagueness? I suppose I could try for something like that. – Ryan Budney Apr 3 '11 at 1:31
• Check out the following paper: The computational complexity of knot genus and spanning area, by Ian Agol, Joel Hass, and William Thurston. Not easy reading, but several of the references are, and the whole field is really pretty. – Sam Nead Jun 27 '11 at 18:11