Contractibility of manifolds by means of stochastic flows

Alexandra Antoniouk; Sergiy Maksymenko

Contractibility of manifolds by means of stochastic flows

Probability 2017-01-12 v3 Algebraic Topology Geometric Topology

Authors: Alexandra Antoniouk , Sergiy Maksymenko

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 in fact under the similar conditions the manifold $M$ is contractible, that is all homotopy groups $\pi_k M$ , $k\geq1$ , vanish.

Keywords

stochastic differential equation moment stability manifold topology contractibility homotopy groups fundamental group

Cite

@article{arxiv.1111.0070,
  title  = {Contractibility of manifolds by means of stochastic flows},
  author = {Alexandra Antoniouk and Sergiy Maksymenko},
  journal= {arXiv preprint arXiv:1111.0070},
  year   = {2017}
}

Comments

9 pages. This version 2 contains a general result about stochastic deformations

Contractibility of manifolds by means of stochastic flows

Abstract

Keywords

Cite

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