Isometry groups of CAT(0) cube complexes

Corey Bregman

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arXiv · 1712.04805

Isometry groups of CAT(0) cube complexes

Corey Bregman

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Abstract

Given a CAT(0) cube complex X, we show that if Aut(X) $\neq$ Isom(X) then there exists a full subcomplex of X which decomposes as a product with $\mathbb{R}^n$. As applications, we prove that if X is $\delta$-hyperbolic, cocompact and 1-ended, then Aut(X) $=$ Isom(X) unless X is quasi-isometric to $\mathbb{H}^2$, and extend the rank-rigidity result of Caprace-Sageev to any lattice $ \Gamma\leq$ Isom(X).

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BibTeX RIS

Corey Bregman. 2017-12-13. Isometry groups of CAT(0) cube complexes. https://arxiv.org/abs/1712.04805

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