Frédéric Haglund works on geometric group theory and cubical geometry. His joint work with Daniel T. Wise introduced special cube complexes and related them to Right-angled Artin groups.[ref]
Special cube complexes by Frédéric Haglund and Daniel T. Wise. Original byline and introduction
The key conditions control how hyperplanes embed, whether they are two-sided and how they meet. A local isometry to a standard cubical model then yields an embedding of the fundamental group. This is a concrete mechanism for obtaining algebraic information from the internal geometry of a complex.[ref]
Special cube complexes by Frédéric Haglund and Daniel T. Wise. Theorem 1.1 and definition of specialness
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