4 papers · 1 filter
Coarse medians and universal quasigeodesic cones
Robert Tang
We show that any universal quasigeodesic cone of uniformly coarse median spaces admits a canonical coarse median structure. As an application, we recover a result of Bowditch which…
Epimorphism classes and relatively maximal metrics in large-scale geometry
Robert Tang
We consider epimorphisms and several variant notions -- split, effective, regular, strong, and extremal -- and determine which of these coincide in the metric coarse and coarsely L…
The metric Rips filtration, universal quasigeodesic cones, and hierarchically hyperbolic spaces
Robert Tang
We introduce a flexible, categorical framework for large-scale geometry that clarifies basic behaviour of the metric Rips filtration and streamlines some constructions in geometric…
Categorical characterisations of quasi-isometric embeddings
Robert Tang
We characterise the (closeness classes of) quasi-isometric embeddings as the regular monomorphisms in the coarsely Lipschitz category, formalising the notion that they are isomorph…