  In the paper [Probab. Theory Relat. Fields, 100 (1994) 417-428] Xue-Mei Li
has shown that the moment stability of an SDE is closely connected with the
topology of the underlying manifold. In particular, she gave sufficient
condition on SDE on a manifold $M$ under which the fundamental group $\pi_1
M=0$. We prove that in fact under the similar conditions the manifold $M$ is
contractible, that is all homotopy groups $\pi_k M$, $k\geq1$, vanish.
