Contractibility of manifolds by means of stochastic flows

Details Contractibility of manifolds by means of stochastic flows Contractibility of manifolds by means of stochastic flows

2011-10-31

arxiv.org/abs/1111.0070v2

Mathematics

Probability

8 pages

Scientific paper

In the paper [Probab. Theory Relat. Fields, 100 (1994) 417-428] Xue-Mei Li studied stability of stochastic differential equations and the interplay between the moment stability of a SDE and 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 same conditions the manifold M is contractible, that is all homotopy groups \pi_k(M), k>0, vanish. The proof follows the arguments of Xue-Mei Li.

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