Rice University

Events at Rice

Thesis Defense

Graduate and Postdoctoral Studies
Mathematics

Speaker: Corey Bregman
Doctoral Candidate

Automorphisms of nonpositively curved cube complexes, right-angled Artin groups, and homology

Wednesday, April 12, 2017
12:00 PM  to 2:00 PM

303  Sewall Hall


We define an integer-valued invariant of special cube complexes called the genus, and prove that having genus one characterizes special cube complexes with abelian fundamental group. Using the genus, we obtain a new proof that the fundamental group of a special cube complex is either free abelian or surjects onto a non-cyclic free group. We also investigate automorphisms of special cube complexes, and give a new geometric proof that the Torelli subgroup for a right-angled Artin group is torsion-free.

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