Noncommutative rings and characteristic classes of foliations, by Igor Nikolaev

The notion of a characteristic fibration is introduced. This fibration consists of a base space M and a set of fibres which are dimension groups associated to a noncommutative ring R. Every dimension group of the fibration is isomorphic to the first Betti group of M with a `positive cone' depending continuously on the fibre. The characteristic fibrations are linked to the codimension 1 regular foliations on M. In particular, we prove that the characteristic classes of such foliations coincide with the Stiefel-Whitney class of M.

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