Homeomorphism groups of countable Stone spaces are coarsely classified: coarsely bounded when there is one maximal point, quasi-isometric to the infinite Hamming cube for several maximal points of successor rank, and coarsely equivalent to the leaves of a countably branching infinite tree in the…
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Coarse geometry of homeomorphism groups: Classifying countable Stone spaces
Homeomorphism groups of countable Stone spaces are coarsely classified: coarsely bounded when there is one maximal point, quasi-isometric to the infinite Hamming cube for several maximal points of successor rank, and coarsely equivalent to the leaves of a countably branching infinite tree in the…