The image of Bott periodicity in cyclic homology

TL;DR

This paper explores the connection between Bott periodicity in topological K-theory and cyclic homology, providing insights into the periodicity and multiplicativity of the bivariant Chern-Connes character.

Contribution

It establishes a theoretical link between Bott periodicity and cyclic homology, enhancing understanding of their interplay in noncommutative geometry.

Findings

Bott periodicity corresponds to natural periodicity in cyclic homology.

The work clarifies the multiplicativity of the bivariant Chern-Connes character.

Provides a foundation for further studies in noncommutative topology.

Abstract

We analyze the relationship between Bott periodicity in topological $K$-theory and the natural periodicity of cyclic homology. This is a basis for understanding the multiplicativity, in odd dimensions, of a bivariant Chern-Connes character from $K$-theory to cyclic theory.