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arXiv · 2505.21029

Strict C(6) complexes

Zachary Munro·Daniel T. Wise
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Abstract

We define strict C(n) small-cancellation complexes, intermediate to C(n) and C(n+1), and we prove groups acting properly cocompactly on a simply-connected strict C(6) complex are hyperbolic relative to a collection of maximal virtually free abelian subgroups of rank 2. We study geometric walls in a simply-connected strict C(6) complex, and we use them to prove a convex cocompact (cosparse) core theorem for (relatively) quasiconvex subgroups of strict C(6) groups. We provide an examples showing the convex cocompact core theorem is false without the strict C(6) assumption.

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Zachary Munro, Daniel T. Wise. 2025-05-27. Strict C(6) complexes. https://arxiv.org/abs/2505.21029

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