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2018 Contractibility of manifolds by means of stochastic flows
Alexandra Antoniouk, Sergiy Maksymenko
Topol. Methods Nonlinear Anal. 52(2): 599-611 (2018). DOI: 10.12775/TMNA.2018.022

Abstract

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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Alexandra Antoniouk. Sergiy Maksymenko. "Contractibility of manifolds by means of stochastic flows." Topol. Methods Nonlinear Anal. 52 (2) 599 - 611, 2018. https://doi.org/10.12775/TMNA.2018.022

Information

Published: 2018
First available in Project Euclid: 6 November 2018

zbMATH: 07051682
MathSciNet: MR3915653
Digital Object Identifier: 10.12775/TMNA.2018.022

Rights: Copyright © 2018 Juliusz P. Schauder Centre for Nonlinear Studies

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Vol.52 • No. 2 • 2018
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