Twisted coefficients on coarse spaces and their corona

To a metric space X we associate a compact topological space \(\nu '({X})\) ${\nu }^{\prime }(X)$ called the corona of X. Then a coarse map \(f:X\rightarrow Y\) $f:X\to Y$ between metric spaces is mapped to a continuous map \(\nu '({f}):\nu '({X})\rightarrow \nu '({Y})\) ${\nu }^{\prime }(f):{\nu }^{\prime }(X)\to {\nu }^{\prime }(Y)$ 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.