Describes Higson corona via coarse ultrafilter quotients to prove faithfulness of corona functor, gives Künneth formula for twisted coarse cohomology, and obtains Gromov boundary as quotient of Higson corona.
Twisted Coefficients on coarse Spaces and their Corona
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abstract
To a metric space $X$ we associate a compact topological space $\nu' X$ called the corona of $X$. Then a coarse map $f:X\to Y$ between metric spaces is mapped to a continuous map $\nu' f:\nu' X\to \nu' Y$ between coronas. Sheaf cohomology on coarse spaces has been introduced in arXiv:1710.06725. We show the functor $\nu'$ preserves and reflects sheaf cohomology.
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math.MG 1years
2019 1verdicts
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Coarse Homotopy on metric Spaces and their Corona
Describes Higson corona via coarse ultrafilter quotients to prove faithfulness of corona functor, gives Künneth formula for twisted coarse cohomology, and obtains Gromov boundary as quotient of Higson corona.