Finiteness and CAT(0) properties of diagram groups

By Daniel S. Farley. 2003

99 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d337d8124e9bf60d095cfd30f6eb7443d5360182

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Combinatorial algebra : syntax and semantics (2014, unknown): “More information about diagram groups can be found in Farley [101, 102] and Guba and Sapir [138, 139].”
Weak hyperbolicity of cube complexes and quasi‐arboreal groups (2011, background): “More generally, Farley gave an action on a CAT(0) cube complex for diagram groups associated to based semigroup presentations [16, 17].”
Proper isometric actions of Thompson's groups on Hilbert space (2003, background): “IMRN International Mathematics Research Notices 2003, No. 45 Proper Isometric Actions of Thompson’s Groups on Hilbert Space Daniel S. Farley”
Hyperbolicities in CAT(0) cube complexes (2017, unknown): “As a consequence, an easy method is given to determine whether or not an element of a diagram group induces a contracting isometry on the CAT(0) cube complex constructed by Farley [Far03].”
Contracting isometries of CAT(0) cube complexes and acylindrical hyperbolicity of diagram groups (2016, methodology): “Below, we detail the construction of this cube complex as explained in [Far03].”
The braided Ptolemy-Thompson group is finitely presented (2005, background): “Farley’s constructi on ([21]) can be carried on in this more general setting to show that T acts on a CAT(0) cubical complex with braid groups as stabilizers.”
Diagram groups and directed 2-complexes: Homotopy and homology (2003, methodology): “We are going to use Farley’s [14] description of the universal cover S̃q(K) of Sq(K).”
Actions of Picture Groups on CAT(0) Cubical Complexes (2005, unknown): “[7] The link of a vertex v in a cubical complex K is a simplicial complex which may be described topologically as the boundary of a small -neighborhood of v in K.”
The Tits Alternative for Cat(0) Cubical Complexes (2004, background): “Indeed, Thompson’s group is not virtually solvable, and contains no rank-2 free subgroup [8], but Thompson’s group acts freely on an infinite-dimensional (yet proper) CAT(0) cubical complex [13].”
The braided Thompson's groups are of type F∞ (2012, result): “f dening our space X, it should be clear how the Stein spaces for F and V would be described with our model. This construction was given in some generality in [Ste92], and was further generalized in [Far03] to get niteness properties (among other things) for a class of groups called diagram groups, ”