Applications of topology to computer science I'd like to write a survey on the applications of Topology in Computer
Science. I plan to cover the history of topological ideas in Computer
Science and also highlight a few current developments.  It would be
extremely helpful if anyone could give input regarding any of the
questions below.


Are there any papers or notes that describe the chronology of the
use of topology in Computer Science?  
What are the most important application of results in Topology to
Computer Science? 
What are the most interesting areas of current work that use
topology to gain insight into computation? 


Thanks!
Personally, I think the most interesting application of topology was the work done by Herlihy and Shavit. They used algebraic topology to characterize asynchronous distributed computation and gave new proofs of important known results and knocked out a number of long-standing open problems. They won the 2004 Godel prize for that work.

"The Topological Structure of Asynchronous Computation"
by Maurice Herlihy and Nir Shavit,
Journal of the ACM, Vol. 46 (1999), 858-923,