Graham Niblo 2026-11-05
Walls separate pairs of points; counting the separating walls gives a pseudometric. Consistent choices of sides become vertices of a cubical space. This transforms separation data into a geometric object on which the group acts, making combinatorial information available to nonpositive-curvature methods.[ref]
Indira Chatterji 2026-11-05
The distinction between a distance and a pseudometric matters here: different points can be separated by no walls. Counting walls still records enough separation information to support a cubical construction and transfer proper-action properties under the paper's hypotheses.[ref]