We describe algorithms to determine extensions of infinite polycyclic groups having certain properties. In particular, we are interested in torsion-free extensions and extensions whose Fitting subgroup has a minimal centre. Then we apply these methods in topological applications. We discuss the calculation of Betti numbers for compact manifolds, and we describe algorithmic approaches in classifying almost Bieberbach groups.
"Computational aspects of group extensions and their applications in topology." Experiment. Math. 11 (2) 183 - 200, 2002.