Contractibility of manifolds by means of stochastic flows

Alexandra Antoniouk, Sergiy Maksymenko



In the paper [Probab.\ Theory Relat.\ Fields, {\bf 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 under similar analytical conditions the manifold $M$ is contractible, that is all homotopy groups $\pi_n M$, $n\geq1$, vanish.


Stochastic flow; $h$-Brownian motion; homotopy type; contractibility

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