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

Shunsuke Sakai; Makoto Sakuma

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

Geometric Topology 2023-03-21 v3 Combinatorics

Authors: Shunsuke Sakai , Makoto Sakuma

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 $W$ .

Keywords

convex geometry convex cones set theory and dimension theory

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@article{arxiv.2302.10500,
  title  = {Combinatorial local convexity implies convexity in finite dimensional CAT(0) cubed complexes},
  author = {Shunsuke Sakai and Makoto Sakuma},
  journal= {arXiv preprint arXiv:2302.10500},
  year   = {2023}
}

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16 pages

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

Abstract

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