Twisted Coefficients on coarse Spaces and their Corona

Abstract

To a metric space $X$ we associate a compact topological space ${\nu }^{\prime }X$ called the corona of $X$. Then a coarse map $f:X\to Y$ between metric spaces is mapped to a continuous map ${\nu }^{\prime }f:{\nu }^{\prime }X\to {\nu }^{\prime }Y$ between coronas. Sheaf cohomology on coarse spaces has been introduced in arXiv:1710.06725. We show the functor ${\nu }^{\prime }$ preserves and reflects sheaf cohomology.

Cited by in corpus (2)

• Coarse Homotopy on metric Spaces and their Corona
• Coarse compactifications of proper metric spaces