Combinatorial local convexity implies convexity in finite dimensional CAT(0) cubed complexes
Sakai, Shunsuke, Makoto Sakuma · arXiv (Cornell University) · 2023
We give a proof to the following theorem, which is well-known among experts: A connected subcomplex $W$ of a finite dimensional CAT(0) cubed complex $X$ is convex if and only if Lk$(v, W)$ is a full subcomplex of Lk$(v, X)$ for every vertex $v$ of $W$.