Homotopy and homology vanishing theorems and the stability of stochastic flows

DOI10.1007/BF02246767zbMATH Open0858.58053arXivdg-ga/9503008OpenAlexW2054066311MaRDI QIDQ1913617

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Publication date: 25 March 1997

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Abstract: We relate stability properties (i.e. moment exponents) of a stochastic dynamical system on a compact manifold $M$ to the homotopy and integral homology groups of $M$. In the special case of gradient Brownian systems associated to isometric immersions of $M$ in Euclidean space, these moment exponents can be estimated in terms of the second fundamental form of the immersion. This yields topological obstructions to isometric immersions generalizing results of Lawson-Simons and others. Our work also places these authors' work into the general framework of Weitzenb"ock formulas.

Full work available at URL: https://arxiv.org/abs/dg-ga/9503008

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