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arxiv: 1904.00380 · v1 · pith:3DBEDJBMnew · submitted 2019-03-31 · 🧮 math.MG · math.GN

Twisted Coefficients on coarse Spaces and their Corona

Elisa Hartmann This is my paper
classification 🧮 math.MG math.GN
keywords coarsespacescohomologycoronametricsheafspacearxiv
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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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  1. Coarse Homotopy on metric Spaces and their Corona

    math.MG 2019-07 unverdicted novelty 5.0

    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.