Automorphisms and homology of non-positively curved cube complexes

Corey Bregman

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arXiv · 1609.03602

Automorphisms and homology of non-positively curved cube complexes

Corey Bregman

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Abstract

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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Corey Bregman. 2016-09-12. Automorphisms and homology of non-positively curved cube complexes. https://arxiv.org/abs/1609.03602

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