Differentiable cyclic cohomology and Hopf algebraic structures in transverse geometry
| dc.creator | Connes, Alain | |
| dc.creator | Moscovici, Henri | |
| dc.date | 2001-02-20 | |
| dc.date | 2001-03-25 | |
| dc.date.accessioned | 2026-07-07T04:40:17Z | |
| dc.date.available | 2026-07-07T04:40:17Z | |
| dc.description | 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. | |
| dc.description | 44 pages, added references | |
| dc.identifier | https://arxiv.org/abs/math/0102167 | |
| dc.identifier | http://arxiv.org/abs/math/0102167 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/60981 | |
| dc.subject | Differential Geometry | |
| dc.subject | Operator Algebras | |
| dc.subject | Quantum Algebra | |
| dc.subject | 58B34, 58B32, 46L87, 81R60 | |
| dc.title | Differentiable cyclic cohomology and Hopf algebraic structures in transverse geometry | |
| dc.type | text |