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arXiv · 1711.01435

Bi-Lipschitz geometry of contact orbits in the boundary of the nice dimensions

Maria Aparecida Soares Ruas·Saurabh Trivedi
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Abstract

Mather proved that the smooth stability of smooth maps between manifolds is a generic condition if and only if the pair of dimensions of the manifolds are 'nice dimensions' while topologically stability is a generic condition in any pair of dimensions. And, by a result of du Plessis and Wall $C^1$-stability is also a generic condition precisely in the nice dimensions. We address the question of bi-Lipschitz stability in this article. We prove that the Thom-Mather stratification is bi-Lipschitz contact invariant in the boundary of the nice dimensions. This is done in two steps: first we explicitly write the contact unimodular strata in every pair of dimensions lying in the boundary of the nice dimensions and second we construct bi-Lipschitz vector fields whose flow provide the bi-Lipschitz contact trivialization in each of the cases.

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Maria Aparecida Soares Ruas, Saurabh Trivedi. 2017-11-04. Bi-Lipschitz geometry of contact orbits in the boundary of the nice dimensions. https://arxiv.org/abs/1711.01435

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