Celebratio Mathematica — Fuchs — Complete Bibliography

Complete Bibliography

Works connected to Andrei M. Gabrielov

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D. B. Fuchs, A. M. Gabrielov, and I. M. Gel’fand: “The Gauss–Bonnet theorem and the Atiyah–Patodi–Singer functionals for the characteristic classes of foliations,” Topology 15 : 2 (1976), pp. 165–188. MR 431199 Zbl 0347.57009 article

We prove in this article some formulae of Gauss–Bonnet kind for the characteristic classes of foliations (see [Bernstein and Rosenfeld 1972; Bott and Haefliger 1972]). Namely, fixing a Riemannian metric on a manifold with a foliation allows one to determine explicitly for each of these characteristic classes a representing differential form (see, for example, [Bott 1972]). If a domain \( X \) with a piecewise smooth boundary transversal to the foliation is given in the manifold, then the integral of such a form over \( X \), corrected by adding the integrals over faces of different dimensions of certain forms depending on the foliation and the metric near \( \partial X \), depends only on the induced metric on \( \partial X \) (and, of course, on the foliation on \( X \)). By using these formulae one can, in particular, extend the definition of the characteristic classes of foliations to the piecewise smooth case.

Andrei M. Gabrielov	Related
Israïl Moiseevich Gelfand	Related