Coarse co-assembly as a ring homomorphism

TL;DR

This paper demonstrates that the coarse co-assembly map between the K-theory of the stable Higson corona and its target ring structure is a ring homomorphism for contractible coarse spaces, revealing new algebraic properties.

Contribution

It establishes that the coarse co-assembly map preserves ring structures, extending previous understanding of its algebraic nature in coarse geometry.

Findings

The K-theory of the stable Higson corona has a canonical ring structure.

The coarse co-assembly map is a ring homomorphism for contractible coarse spaces.

The target of the co-assembly map also carries a compatible ring structure.

Abstract

The $K$-theory of the stable Higson corona of a coarse space carries a canonical ring structure. This ring is the domain of an unreduced version of the coarse co-assembly map of Emerson and Meyer. We show that the target also carries a ring structure and co-assembly is a ring homomorphism, provided that the given coarse space is contractible in a coarse sense.