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Displaying similar documents to “Doubles of groups and hyperbolic LERF 3-manifolds.”

The geometry of abstract groups and their splittings.

Charles Terence Clegg Wall (2003)

Revista Matemática Complutense

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A survey of splitting theorems for abstract groups and their applications. Topics covered include preliminaries, early results, Bass-Serre theory, the structure of G-trees, Serre's applications to SL and length functions. Stallings' theorem, results about accessibility and bounds for splittability. Duality groups and pairs; results of Eckmann and collaborators on PD groups. Relative ends, the JSJ theorems and the splitting results of Kropholler and Roller on PD groups. Notions of quasi-isometry,...

Structure of geodesics in the Cayley graph of infinite Coxeter groups

Ryszard Szwarc (2003)

Colloquium Mathematicae

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Let (W,S) be a Coxeter system such that no two generators in S commute. Assume that the Cayley graph of (W,S) does not contain adjacent hexagons. Then for any two vertices x and y in the Cayley graph of W and any number k ≤ d = dist(x,y) there are at most two vertices z such that dist(x,z) = k and dist(z,y) = d - k. Allowing adjacent hexagons, but assuming that no three hexagons can be adjacent to each other, we show that the number of such intermediate vertices at a given distance from...

A short proof of a theorem of Brodskii.

James Howie (2000)

Publicacions Matemàtiques

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A short proof, using graphs and groupoids, is given of Brodskii’s theorem that torsion-free one-relator groups are locally indicable.