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Title: The Parallel Wall Theorem for CAT(0) even 2-complexes

Abstract: The Parallel Wall Theorem for Coxeter groups, first introduced by Davis-Shapiro and proven by Brink-Howlett, establishes a finiteness property for walls in Coxeter groups, i.e. the fixed point sets in $\text{Cay}(W, S)$ of reflections in the Coxeter group $(W, S)$. The theorem states that there is a bound $K$, depending only on the Coxeter group $(W, S)$, such that, for any element $w\in W$ and wall $\mathcal{W}$ at distance $\geq K$ from $w$, there is another wall in $(W, S)$ separating $w$. We prove the analogous statement for CAT(0) even 2-complexes, i.e. 2-complexes built out of even-sided regular polygons whose piecewise Euclidean metric is CAT(0).

We will gather for teatime in the lounge at 4pm after the talk.

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