Topology of the C*-algebra bundles, by Igor Nikolaev

Abstract: Using the methods of the noncommutative geometry and the K-theory, we prove that the well-known Dixmier-Douady invariant of continuous-trace C^*-algebras and the Godbillon-Vey invariant of the codimension-1 foliations on compact manifolds coincide in a class of the so-called "foliation derived" C^*-algebra bundles. Moreover, with the help of such bundles both of the above invariants admit an elegant interpretation as Pontrjagin's invariants of the homotopy equivalent mappings of the three-dimensional complex into the two-dimensional sphere.

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Igor Nikolaev <nikolaev@math.uqam.ca>