Hopf Algebras, Cyclic Cohomology and the Transverse Index Theorem

摘要: In this paper we solve a longstanding internal problem of noncommutative geometry, namely the computation index transversally elliptic operators on foliations. We show that local formula for hypoelliptic can be settled thanks to very specific Hopf algebra \(\), associated each integer codimension. This reduces transverse universal geometry affine nature. The structure algebra, its relation with Lie formal vector fields as well cyclic cohomology are done in present paper, which also under suitable unimodularity condition cosimplicial space underlying Hochschild carries highly nontrivial structure.