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B Γ

Francis Sergeraert (1977/1978)

Séminaire Bourbaki

Bi-Legendrian connections

Beniamino Cappelletti Montano (2005)

Annales Polonici Mathematici

We define the concept of a bi-Legendrian connection associated to a bi-Legendrian structure on an almost -manifold M 2 n + r . Among other things, we compute the torsion of this connection and prove that the curvature vanishes along the leaves of the bi-Legendrian structure. Moreover, we prove that if the bi-Legendrian connection is flat, then the bi-Legendrian structure is locally equivalent to the standard structure on 2 n + r .

Bilipschitz invariance of the first transverse characteristic map

Michel Hilsum (2012)

Banach Center Publications

Given a smooth S¹-foliated bundle, A. Connes has shown the existence of an additive morphism ϕ from the K-theory group of the foliation C*-algebra to the scalar field, which factorizes, via the assembly map, the Godbillon-Vey class, which is the first secondary characteristic class, of the classifying space. We prove the invariance of this map under a bilipschitz homeomorphism, extending a previous result for maps of class C¹ by H. Natsume.

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