PUB - Publikationen an der Universität Bielefeld

To a metric space X we associate a compact topological space nu ' ( X ) \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\nu '({X})$$\end{document} called the corona of X. Then a coarse map f : X -> Y \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f:X\rightarrow Y$$\end{document} between metric spaces is mapped to a continuous map nu ' ( f ) : nu ' ( X ) -> nu ' ( Y ) \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\nu '({f}):\nu '({X})\rightarrow \nu '({Y})$$\end{document} 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.