Finitely presented groups with k-planar Cayley graphs have finite-index subgroups with planar Cayley graphs; k-planar coarsely simply connected quasi-transitive graphs are quasi-isometric to planar graphs.
Boundaries of hyperbolic g roups
2 Pith papers cite this work. Polarity classification is still indexing.
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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.
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Almost planar finitely presented groups
Finitely presented groups with k-planar Cayley graphs have finite-index subgroups with planar Cayley graphs; k-planar coarsely simply connected quasi-transitive graphs are quasi-isometric to planar graphs.
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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.