Coarse Homotopy on metric Spaces and their Corona
Elisa Hartmann
TL;DR
This paper explores the Higson corona of metric spaces, demonstrating its faithfulness, deriving a K"unneth formula for twisted coarse cohomology, and relating the Gromov boundary to the Higson corona.
Contribution
It introduces a quotient description of the Higson corona, proving the corona functor's faithfulness and establishing a new K"unneth formula for twisted coarse cohomology.
Findings
Higson corona can be described via coarse ultrafilters.
The corona functor is shown to be faithful.
A K"unneth formula for twisted coarse cohomology is derived.
Abstract
This paper discusses properties of the Higson corona by means of a quotient on coarse ultrafilters on a proper metric space. We use this description to show that the corona functor is faithful. This study provides a K\"unneth formula for twisted coarse cohomology. We obtain the Gromov boundary of a hyperbolic proper geodesic metric space as a quotient of its Higson corona.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Advanced Operator Algebra Research