Embedding of Higson compactification into the product of adelic solenoids

TL;DR

This paper demonstrates that the Higson compactification of certain metric spaces can be embedded into a product of adelic solenoids, preserving their 1-dimensional cohomology structure.

Contribution

It introduces an embedding of Higson compactification into adelic solenoids that induces cohomology isomorphism, linking geometric and algebraic structures.

Findings

Embedding into adelic solenoids preserves 1-dimensional cohomology.

The Higson compactification can be represented within a product of adelic solenoids.

The approach connects geometric compactifications with algebraic topological invariants.

Abstract

The Higson compactification of any simply connected proper geodesic metric space admits an embedding into a product of adelic solenoids that induces an isomorphism of 1-dimensional cohomology.