Effective Homology of Universal Covers.

We present an algorithm for constructing the e.ective homology for the universal cover of simplicial sets with e.ective homology, provided that a nilpotency condition holds. This can be useful for computing higher homotopy groups, since this process can be seen as the first step in the Whitehead tower. Our algorithm can be applied to some spaces satisfying a particular condition. We also present implementations of this method in SageMath and Kenzo.