Entire cyclic cohomology of Schatten ideals

Excision in Entire Cyclic Cohomology

An extension of bornological algebras with a bounded linear section gives rise to a six term exact sequence of the associated periodic and entire cyclic cohomology groups. 1. Introduction A convex vector bornology on a vector space is a collection of subsets satisfying some conditions 8]. A typical example is the collection of bounded subsets of a locally convex vector space. A bornological alg...

Simplicial normalization in the entire cyclic cohomology of Banach algebras

We show that the entire cyclic cohomology of Banach algebras defined by Connes has the simplicial normalization property. A key tool in the proof is the notion and properties of supertraces on the Cuntz algebra QA. As an example of further applications of this technique we give a proof of the homotopy invariance of entire cyclic cohomology.

The equivariant index theorem in entire cyclic cohomology

Let G be a locally compact group acting smoothly and properly by isometries on a complete Riemannian manifoldM , with compact quotient GnM . There is an assembly map W K .M/ ! K .B/ which associates to any Gequivariant K-homology class onM , an element of the topological K-theory of a suitable Banach completion B of the convolution algebra of continuous compactly supported functions on G. The a...

Local Cohomology at Monomial Ideals

Division of Entire Functions by Polynomial Ideals

In [ASTW] it was given a Grobner reduction based division formula for entire functions by polynomial ideals. Here we give degree bounds where the input function can be truncated in order to compute approximations of the coe cients of the power series appearing in the division formula within a given precision. In addition, this method can be applied to the approximation of the value of the rema...