We derive an estimate of the lower boundary of the conformal window of SP (2N) and SO(N) gauge theories with fermionic matter in several different representations. We calculate the index of topological excitations for these groups on the manifold R3 × S1, from which we deduce the scale of the generation of the mass gap of the theory. This is then used to approximate the critical value of the number of species nf for the onset of conformality on R4. We also provide a detailed comparison with other estimates of the conformal window. ∗Changing to email@example.com as of October 1 2009.