Daniel T. Wise studies geometric group theory through cubical geometry. With Frédéric Haglund, he introduced and studied special cube complexes, whose hyperplanes satisfy restrictions preventing certain self-interactions.[ref]
Special cube complexes by Frédéric Haglund and Daniel T. Wise. Original byline, introduction and Theorem 1.1
A compact nonpositively curved cube complex satisfying their criterion admits a local isometry into the standard complex of a Right-angled Artin group. Consequently its fundamental group embeds in a linear group. The contribution connects visible geometric conditions on hyperplanes with algebraic properties of the fundamental group.[ref]
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