Transgressing the algebraic coarse character map

TL;DR

This paper investigates a conjecture relating the algebraic K-theory of finite propagation operators to the Higson corona, showing that the algebraic coarse character map transgresses to the classical Chern character.

Contribution

It proves that transgressing the algebraic coarse character map on finite propagation operators aligns with the Chern character on the Higson corona, confirming a conjecture of John Roe.

Findings

Confirmed the conjecture relating algebraic K-theory and the Chern character.

Established the transgression of the algebraic coarse character map to the Higson corona.

Connected algebraic K-theory with classical topological invariants.

Abstract

We pursue an old conjecture of John Roe about the algebraic K-theory of the algebra of finite propagation, locally trace-class operators, namely that transgressing the algebraic coarse character map on this algebra to a Higson dominated corona coincides with the usual Chern character on the corona.