DETECTING $K$-THEORY BY CYCLIC HOMOLOGY

Detecting K-theory by Cyclic Homology

We discuss which part of the rationalized algebraic K-theory of a group ring is detected via trace maps to Hochschild homology, cyclic homology, periodic cyclic or negative cyclic homology.

On the K · Theory and Cyclic Homology of a Square

The purpose of this paper is to establish an integral connection between the relative K-theory and cyclic homology of a square-zero ideal IeR, R a ring with unit. We restrict attention to the case when R is a split extension of R/I by I. The outline of the paper is as follows: in Section 2, we compute a direct summand of HC*(R, I), where HC*(R, 1) is graded in analogy to relative K-theory and f...

Pro cdh-descent for cyclic homology and K-theory

In this paper we prove that cyclic homology, topological cyclic homology, and algebraic K-theory satisfy a pro Mayer–Vietoris property with respect to abstract blow-up squares of varieties, in both zero and finite characteristic. This may be interpreted as the well-definedness of K-theory with compact support.

Cyclic Homology Theory, Part II

TWISTED K - HOMOLOGY THEORY , TWISTED Ext - THEORY

These are notes on twisted K-homology theory and twisted Ext-theory from the C *-algebra viewpoint, part of a series of talks on " C *-algebras, noncommutative geometry and K-theory " , primarily for physicists.