Mathematics – Differential Geometry
Scientific paper
2001-02-20
Mathematics
Differential Geometry
44 pages, added references
Scientific paper
We prove a cyclic cohomological analogue of Haefliger's van Est-type theorem for the groupoid of germs of diffeomorphisms of a manifold. The differentiable version of cyclic cohomology is associated to the algebra of transverse differential operators on that groupoid, which is shown to carry an intrinsic Hopf algebraic structure. We establish a canonical isomorphism between the periodic Hopf cyclic cohomology of this extended Hopf algebra and the Gelfand-Fuchs cohomology of the Lie algebra of formal vector fields. We then show that this isomorphism can be explicitly implemented at the cochain level, by a cochain map constructed out of a fixed torsion-free linear connection. This allows the direct treatment of the index formula for the hypoelliptic signature operator - representing the diffeomorphism invariant transverse fundamental $K$-homology class of an oriented manifold - in the general case, when this operator is constructed by means of an arbitrary coupling connection.
Connes Alain
Moscovici Henri
No associations
LandOfFree
Differentiable cyclic cohomology and Hopf algebraic structures in transverse geometry does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Differentiable cyclic cohomology and Hopf algebraic structures in transverse geometry, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Differentiable cyclic cohomology and Hopf algebraic structures in transverse geometry will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-520357