Left coarse structure on G/H is not always the quotient of that on G; counterexample in mapping class groups of Loch Ness monster surfaces, plus conditions involving bounded-set liftings, transversals, and metrisability.
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Coarse Structures on Homogeneous Spaces
Left coarse structure on G/H is not always the quotient of that on G; counterexample in mapping class groups of Loch Ness monster surfaces, plus conditions involving bounded-set liftings, transversals, and metrisability.