The original posting was kind of vague and misleading, but there are a number of connections between topology and computer science. For some involving computational geometry, you might want to check out a report I co-authored, "Emerging challenges in computational topology", http://arXiv.org/abs/cs.CG/9909001
Other connections include
- Graph theory sprang out of topology, and is central to theoretical computer science.
- Topological invariants have been used to provide lower bounds on the amount of computing time needed to solve various problems. A standard example is the problem of determining whether any two of n numbers are equal to another -- the set of n-tuples with two equal disconnects the set of all other n-tuples into n! connected components, from which one can conclude that log_2(n!)=Omega(n log n) time is required in certain models of computation -- of course one can use hashing to solve this sort of problem more quickly but that would be outside these models.
- Topological analysis of distributed computation (about which I don't know much, sorry) -- David Eppstein UC Irvine Dept. of Information & Computer Science email@example.com http://www.ics.uci.edu/~eppstein/