A combination theorem for special cube complexes.

DOI10.4007/annals.2012.176.3.2zbMath1277.20046OpenAlexW2126761065WikidataQ56519834 ScholiaQ56519834MaRDI QIDQ1928612

Frédéric Haglund, Daniel T. Wise

Publication date: 3 January 2013

Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4007/annals.2012.176.3.2

zbMATH Keywords

graphs of groupsright-angled Artin groupsresidual finitenessCAT(0) cube complexesword-hyperbolic groupsvirtually special complexes

Mathematics Subject Classification ID

Geometric group theory (20F65) Braid groups; Artin groups (20F36) Topological methods in group theory (57M07) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations (20E06) Hyperbolic groups and nonpositively curved groups (20F67) Residual properties and generalizations; residually finite groups (20E26)

Related Items (32)

Imitator homomorphisms for special cube complexes ⋮ Cubulation of some triangle-free Artin groups ⋮ Combination Theorems in Groups, Geometry and Dynamics ⋮ Virtual Retraction Properties in Groups ⋮ AN ALTERNATE PROOF OF WISE’S MALNORMAL SPECIAL QUOTIENT THEOREM ⋮ Residual finiteness of certain 2-dimensional Artin groups ⋮ A combination theorem for cubulation in small cancellation theory over free products ⋮ Right-angled Artin groups on finite subgraphs of disk graphs ⋮ Quasiconvexity and relatively hyperbolic groups that split. ⋮ Non-hyperbolic automatic groups and groups acting on CAT(0) cube complexes ⋮ When does a right-angled Artin group split over ℤ? ⋮ Commensurability of groups quasi-isometric to RAAGs ⋮ A counterexample to Thiagarajan's conjecture on regular event structures ⋮ On cubulated relatively hyperbolic groups ⋮ No quasi-isometric rigidity for proper actions on CAT(0) cube complexes ⋮ Semistability of cubulated groups ⋮ RAAGs in Ham ⋮ Relatively geometric actions on CAT$\operatorname{CAT}$(0) cube complexes ⋮ Virtual specialness of certain graphs of special cube complexes ⋮ Projection complexes and quasimedian maps ⋮ Homology growth, hyperbolization, and fibering ⋮ Abelian splittings of right-angled Artin groups ⋮ The Poincaré Conjecture and Related Statements ⋮ Complexes of groups and geometric small cancelation over graphs of groups ⋮ Hyperfiniteness of boundary actions of cubulated hyperbolic groups ⋮ Cubulating malnormal amalgams. ⋮ Residual finiteness growths of virtually special groups. ⋮ Relative cubulations and groups with a 2-sphere boundary ⋮ Quasi-isometry invariants of weakly special square complexes ⋮ Cross ratios and cubulations of hyperbolic groups ⋮ Geometric group theory and 3-manifolds hand in hand: the fulfillment of Thurston’s vision ⋮ Cross‐ratios on CAT(0) cube complexes and marked length‐spectrum rigidity

Cites Work

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• Separable subsets of GFERF negatively curved groups.
• Coxeter groups are virtually special
• Packing subgroups in relatively hyperbolic groups.
• Ping-pong on negatively curved groups
• The residual finiteness of negatively curved polygons of finite groups.
• Embeddings of Gromov hyperbolic spaces
• On groups acting on nonpositively curved cubical complexes
• The Bianchi groups are separable on geometrically finite subgroups.
• Special cube complexes
• Embedding of hyperbolic spaces in the product of trees
• Subgroups of Surface Groups are Almost Geometric
• Widths of Subgroups
• Ends of Group Pairs and Non-Positively Curved Cube Complexes
• Subgroup Separability of Graphs of Free Groups with Cyclic Edge Groups
• Hyperplane sections in arithmetic hyperbolic manifolds
• Finiteness properties of cubulated groups

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