Title: Iteration of functions and contractibility of 
acyclic 2-complexes 

Author:  Ian J Leary 

Affiliation:  University of Southampton.  

Abstract:  We show that there can be no algorithm to decide
whether infinite recursively described acyclic aspherical 
2-complexes are contractible.  We construct such a complex
that is contractible if and only if the Collatz conjecture 
holds.