Abstract

A contact structure on a three-dimensional manifold is a two-dimensional distribution on this manifold which satisfies the condition of complete non-integrability. If the distribution fails to satisfy this condition at points of some submanifold, we have a contact structure with singularities. The singularities of contact structures were studied by J. Martinet, B. Jakubczyk and M. Zhitomirskii. We consider a contact structure with singularities as a \(G\)-structure with singularities, we find some topological and differential invariants of singularities of contact structure and establish their relation to the invariants found by B. Jakubczyk and M. Zhitomirskii.

中文翻译：

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三维流形上接触结构奇异性的拓扑和微分不变性

摘要

三维歧管上的接触结构是该歧管上的二维分布，它满足完全不可积的条件。如果分布在某些子流形的点上不满足此条件，则我们具有奇异的接触结构。接触结构的奇异性由J. Martinet，B。Jakubczyk和M.Zhitomirskii研究。我们将具有奇异性的接触结构视为具有奇异性的\（G \）-结构，我们发现了接触结构奇异性的一些拓扑和差分不变量，并建立了它们与B. Jakubczyk和M. Zhitomirskii发现的不变量的关系。