Cartan connection and characteristic classes of foliations

Noncommutative rings and characteristic classes of foliations

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 ...

Characteristic Classes of Transversely Homogeneous Foliations

The foliations studied in this paper have transverse geometry modeled on a homogeneous space G/H with transition functions given by the left action of G. It is shown that the characteristic classes for such a foliation are determined by invariants of a certain flat bundle. This is used to prove that when G is semisimple, the characteristic classes are rigid under smooth deformations, extending ...

Equivariant Characteristic Classes in the Cartan Model

This note shows the compatibility of the differential geometric and the topological formulations of equivariant characteristic classes for a compact connected Lie group action. Suppose G and S are two compact Lie groups, and P and M are manifolds. A principal G-bundle π : P → M is said to be S-equivariant if S acts on the left on both P and M in such a way that a) the projection map π is S-equi...

Algebraic Theory of Characteristic Classes of Bundles with Connection

On some classes of foliations

The goal of the paper is to present in a unitary way some conditions that a foliation be Riemannian, involving general conditions on higher order normal bundles (jets or accelerations). M.S.C. 2010: 53C12, 57R10, 55R10, 55R15, 58A20.