Coarse compactifications and controlled products

Abstract

We introduce the notion of controlled products on metric spaces as a generalization of Gromov products, and construct boundaries by using controlled products, which we call the Gromov boundaries. It is shown that the Gromov boundary with respect to a controlled product on a proper metric space complements the space as a coarse compactification. It is also shown that there is a bijective correspondence between the set of all coarse equivalence classes of controlled products and the set of all equivalence classes of coarse compactifications.

arXiv comment22 pages

References in corpus (2)

• A coarse Cartan-Hadamard theorem with application to the coarse Baum-Connes conjecture
• Coronae of product spaces and the Coarse Baum-Connes conjecture

Cited by in corpus (1)

• Coarse compactifications of proper metric spaces