Twisted coefficients on coarse spaces and their corona

Abstract

To a metric space X we associate a compact topological space $$\nu '({X})$$ ν ′ ( X ) called the corona of X. Then a coarse map $$f:X\rightarrow Y$$ f : X → Y between metric spaces is mapped to a continuous map $$\nu '({f}):\nu '({X})\rightarrow \nu '({Y})$$ ν ′ ( f ) : ν ′ ( X ) → ν ′ ( Y ) between coronas. Sheaf cohomology assigned to a coarse metric space is preserved and reflected by the corona functor. This work reveals new tools to analyze the Higson corona.