Topological Methods in Nonlinear Analysis

Contractibility of manifolds by means of stochastic flows

Alexandra Antoniouk and Sergiy Maksymenko

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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 under similar analytical conditions the manifold $M$ is contractible, that is all homotopy groups $\pi_n M$, $n\geq1$, vanish.

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Topol. Methods Nonlinear Anal., Volume 52, Number 2 (2018), 599-611.

First available in Project Euclid: 6 November 2018

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Antoniouk, Alexandra; Maksymenko, Sergiy. Contractibility of manifolds by means of stochastic flows. Topol. Methods Nonlinear Anal. 52 (2018), no. 2, 599--611. doi:10.12775/TMNA.2018.022.

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