Coning-off CAT(0) cube complexes
نویسندگان
چکیده
In this paper, we study the geometry of cone-offs CAT(0) cube complexes over a family combinatorially convex subcomplexes, with an emphasis on their Gromov-hyperbolicity. A first application gives direct cubical proof characterization (strong) relative hyperbolicity right-angled Coxeter groups, which is particular case result due to Behrstock, Caprace, Hagen and Sisto. second acylindrical C ′ (1/4)-T(4) small cancellation quotients free products.
منابع مشابه
Non-positively Curved Cube Complexes
Let Γ be a discrete group, defined by a presentation P = 〈ai | rj〉, say, or as the fundamental group of a connected CW-complex X. Remark 1.1. Let XP be the CW-complex with a single 0-cell E , one 1-cell E i for each ai (oriented accordingly), and one 2-cell E 2 j for each rj , with attaching map ∂E j → X (1) P that reads off the word rj in the generators {ai}. Then, by the Seifert–van Kampen Th...
متن کاملStallings’ folds for cube complexes
We describe a higher dimensional analogue of Stallings’ folding sequences for group actions on CAT(0) cube complexes. We use it to give a characterization of quasiconvex subgroups of hyperbolic groups that act properly co-compactly on CAT(0) cube complexes via finiteness properties of their hyperplane stabilizers.
متن کاملCube-like Polytopes and Complexes
The main purpose of this paper is to popularize Danzer’s power complex construction and establish some new results about covering maps between two power complexes. Power complexes are cube-like combinatorial structures that share many structural properties with higher-dimensional cubes and cubical tessellations on manifolds. Power complexes that are also abstract polytopes have repeatedly appea...
متن کاملPing Pong on Cat ( 0 ) Cube Complexes
Let G be a group acting properly and essentially on an irreducible, non-Euclidean finite dimensional CAT(0) cube complex X without a global fixed point at infinity. We show that for any finite collection of simultaneously inessential subgroups {H1, . . . , Hk} in G, there exists an element g of infinite order such that ∀i, 〈Hi, g〉 ∼= Hi ∗ 〈g〉. We apply this to show that any group, acting faithf...
متن کاملIsometry Groups of Cat(0) Cube Complexes
Given a CAT(0) cube complex X, we show that if Aut(X) 6= Isom(X) then there exists a full subcomplex of X which decomposes as a product with R. As applications, we prove that ifX is δ-hyperbolic, cocompact and 1-ended, then Aut(X) = Isom(X) unless X is quasi-isometric to H, and extend the rank-rigidity result of Caprace–Sageev to any lattice Γ ≤ Isom(X).
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Annales de l'Institut Fourier
سال: 2021
ISSN: ['0373-0956', '1777-5310']
DOI: https://doi.org/10.5802/aif.3430