Graham Niblo works on geometric group theory. With Indira Chatterji, he explained a construction taking a group action on a wallspace to an action on a CAT(0) cube complex.[ref]
From wall spaces to CAT(0) cube complexes by Indira Chatterji and Graham Niblo. Original byline and abstract
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]
From wall spaces to CAT(0) cube complexes by Indira Chatterji and Graham Niblo. Section 1, pp. 2–3, and construction
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