Before revision:  On the other hand, there are several algorithms that, given a finite simplicial complex X that is simply connected (i.e., with \pi_1(X) trivial), compute the higher homotopy group \pi_d(X) for any given d\geq 2. \%The first such algorithm was given by Brown, and more recently, Cadek et al.
After revision:  On the other hand, there are several algorithms that, given a finite simplicial complex X that is simply connected (i.e., with \pi_1(X) trivial), compute the higher homotopy group \pi_d(X) for any given d\geq 2. \%The first such algorithm was given by Brown, and more recently, Cadek et al.