Thomsen's D-theory and the K-theoretic Kronecker pairing

TL;DR

This paper computes Thomsen's D-theory groups for a specific algebra and relates a K-theoretic pairing to a similar pairing defined via D-theory, advancing understanding in operator K-theory.

Contribution

It provides explicit calculations of D-theory groups for the algebra C_0(R) and connects K-theoretic pairings with D-theory, offering new insights into their relationship.

Findings

Calculated D-theory groups for C_0(R).

Established a connection between K-theoretic pairings and D-theory.

Enhanced understanding of pairings in operator K-theory.

Abstract

We calculate Thomsen's D-theory groups $D(\Sigma,B)$, where $\Sigma=C_0(\mathbb R)$. Furthermore, we relate the pairing $K_0(A)\times E(A,B)\to K_0(B)$ to a similar pairing which is defined using D-theory.