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The University of Southampton
Mathematical Sciences

Research project: The coarse geometry of CAT(0) cube complexes

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CAT(0) cubical complexes play a central role in geometric group theory, arising naturally from the study of right angled Artin groups, Coxeter groups, certain knot groups and limit groups.

In a series of papers we studied the asymptotic Hilbert space compression of these spaces and showed that they satisfy Yu’s generalized amenability condition of property A. In the latest result we showed that for groups acting on finite dimensional CAT(0) cube complexes property A is inherited from the vertex stabilisers. As an interesting side effect we showed that if a group acts properly on a finite dimensional CAT(0) cube complex then stabilisers at infinity are amenable

Related research groups

Pure Mathematics

Key Publications

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