  We prove that all SYM theories that have a quantum modified moduli space $\m$
defined by a single constraint equation have trivial homotopy groups
$\pi_j(\m)$ 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.
