Cubulating small cancellation groups

By Daniel T. Wise. 2004

193 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/cdb380541f38b4bec79a23ca00e504d548849c1e

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Hierarchically hyperbolic spaces I: curve complexes for cubical groups (2014, background): “oups [Dav08, NR03], right-angled Artingroups[CD95],and,moregenerally,graphproductsofabeliangroups[RW]. Otherexamplesofcubicalgroupsinclude: groupssatisfyingsuﬃcientlystrongsmall-cancellationconditions[Wis04];many3–manifoldgroups,includingallhyperbolicones[KM09,BW13,Wis] andsomegraphmanifoldgroups[HP”
Property A and CAT(0) cube complexes (2009, background): “These spaces, which are generalizations of (products of simplicial) trees, appear naturally in many problems in geometric group theory and low dimensional topology [AR90, HW07, Sag97, Wis04 ].”
Coxeter groups are virtually special (2010, unknown): “MSC: 53C23; 20F36; 20F55; 20F67; 20F65; 20E26 Keywords: CAT(0) cube complexes; Coxeter group; Artin group; Subgroup separability”
Cubulating random groups at density less than 1/6 (2011, unknown): “Consequently, at density , the groups will not have Property ( T ) since C ( ) groups act properly discontinuously on CAT(0) cube complexes [Wis04].”
Weak hyperbolicity of cube complexes and quasi‐arboreal groups (2011, background): “(1) Finitely presented groups satisfying the B(4) − T (4) small-cancelation condition act properly and cocompactly on CAT(0) cube complexes, and B(6) groups act properly on CAT(0) cube complexes with finitely many orbits of hyperplanes [35].”
Isometries of CAT(0) cube complexes are semi-simple (2007, result): “This complex was introduced simultaneously in [2, 10], thus generalizing the previous constructions of [11] and [13].”
Determining Fuchsian groups by their finite quotients (2014, background): “Wise [56] proves that the hyperbolic group Γ is the fundamental group of a compact non-positively curved cube complex, and Agol [1] proves that such groups are linear, hence residually-finite.”
Special Cube Complexes (2008, methodology): “For instance, in [NR] his construction is used to show that word-hyperbolic Coxeter groups act properly discontinuously and cocompactly on CAT(0) cube complexes, and the same is shown for finitely presented C � (1/6) small-cancellation groups in [ Wi6 ].”
Isometry groups of non‐positively curved spaces: discrete subgroups (2009, background): “Amongst the examples arising in this way are hyperbolic Coxeter groups [69], C ′( (1)6 ) and C ′( (1)4 )-T (4) small cancellation groups [92], and 2-dimensional 7systolic groups [53].”
Combinatorial algebra : syntax and semantics (2014, unknown): “One of the strongest results about small cancelation groups has been obtained recently by Ian Agol [10] (based on the work of Daniel Wise [330]).”
Hyperbolicities in CAT(0) cube complexes (2017, unknown): “In [Wis04], Wise shows how to endow every small cancellation polygonal complex with a structure of space with walls.”
The Tits Alternative for Cat(0) Cubical Complexes (2004, background): “Indeed, fundamental groups of compact C ′( 16 ) and C ′( 14 )–T (4) complexes act with uniformly bounded stabilizers on finite-dimensional CAT(0) cube complexes [22].”