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arXiv · 2210.06378

Random Group Actions on $\mathrm{CAT}(0)$ Square Complexes

Zachary Munro
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Abstract

We generalize ideas of Jahncke from trees to square complexes. We introduce the notion of progression in $\mathrm{CAT}(0)$ square complexes. Using progression, we are able to build on the proof strategy of Dahmani-Guirardel-Przytycki to show any action of a random group with seven or more generators on a $\mathrm{CAT}(0)$ square complex has a global fixed point.

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Zachary Munro. 2022-10-12. Random Group Actions on $\mathrm{CAT}(0)$ Square Complexes. https://arxiv.org/abs/2210.06378

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