[en] We prove that all SYM theories that have a quantum modified moduli space M defined by a single constraint equation have trivial homotopy groups π_j (M) for j = 0,1,2,3 and 4. This implies that none of these theories admit skyrmions or vortexes -a fact that had only been proved for supersymmetric QCD with N _f = N _c and Sp(2N) with 2N+2 fundamentals- whereas those of them with a nontrivial H ⁵(M) admit Wess-Zumino-Witten terms in their effective actions. Contrary to expectations, examples of quantum modified moduli spaces with a trivial H ⁵(M) are found in the literature. (author)