Hopf algebras, cyclic cohomology and the transverse index theory

Details Hopf algebras, cyclic cohomology and the transverse index theory Hopf algebras, cyclic cohomology and the transverse index theory

1998-06-19

arxiv.org/abs/math/9806109v1

Mathematics

Differential Geometry

54 pages

Scientific paper

10.1007/s002200050477

We present the solution of a longstanding internal problem of noncommutative geometry, namely the computation of the index of a transversally elliptic operator on an arbitrary foliation. The new and crucial ingredient is a certain Hopf algebra associated to the transverse frame bundle. Its cyclic cohomology is defined and shown to be canonically isomorphic to the Gelfand-Fuks cohomology.

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