Combinatorial local convexity implies convexity in finite dimensional CAT(0) cubed complexes

Shunsuke Sakai; Makoto Sakuma

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arXiv · 2302.10500

Combinatorial local convexity implies convexity in finite dimensional CAT(0) cubed complexes

Shunsuke Sakai·Makoto Sakuma

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Abstract

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 $W$.

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BibTeX RIS

Shunsuke Sakai, Makoto Sakuma. 2023-02-21. Combinatorial local convexity implies convexity in finite dimensional CAT(0) cubed complexes. https://arxiv.org/abs/2302.10500

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