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Cubical quotients of cubical nonproducts

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NPCW06 - Non-positive curvature and applications

Burger-Mozes constructed examples of simple groups acting geometrically on a CAT complex, which is a product of trees. As a counterpoint, we prove that every group acting geometrically on a CAT cube complex which is not a product, admits a nontrivial quotient which also admits a geometric action on a CAT cube complex. Our construction relies on the cubical version of small cancelation theory. This is joint work with M. Arenas and D. Wise.  

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