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Register a new userTwisted Coefficients on coarse Spaces and their Corona
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Authors
Elisa Hartmann
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To a metric space $X$ we associate a compact topological space $ u X$ called the corona of $X$. Then a coarse map $f:Xto Y$ between metric spaces is mapped to a continuous map $ u f: u Xto u Y$ between coronas. Sheaf cohomology on coarse spaces has been introduced in arXiv:1710.06725. We show the functor $ u$ preserves and reflects sheaf cohomology.
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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 Kunneth 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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