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- W Dicks
- 2006

The axiomatic definition of the group concept packs so much power in a small space that it has sometimes overshadowed the geometric aspects. But groups have from their beginnings played an important role in geometry, and the geometrical applications have in their turn contributed to our knowledge of groups. Thus Cayley in 1878 [1] described what has come to… (More)

We use elementary methods to compute the L 2-dimension of the eigen-spaces of the Markov operator on the lamplighter group and of generalizations of this operator on other groups. In particular, we give a transparent explanation of the spectral measure of the Markov operator on the lamp-lighter group found by Grigorchuk-Zuk [4]. The latter result was used… (More)

- WARREN DICKS, IAN J. LEARY, Ronald M. Solomon
- 1998

Recently, M. Bestvina and N. Brady have exhibited groups that are of type F P but not finitely presented. We give explicit presentations for groups of the type considered by Bestvina-Brady. This leads to algebraic proofs of some of their results. Let ∆ be a finite flag complex, that is, a finite simplicial complex that contains a simplex bounding every… (More)

- R. C. Alperin, W. Dicks, J. Porti
- 1998

We give an elementary proof of the Cannon-Thurston Theorem in the case of the Gieseking manifold. We work entirely on the boundary, using ends of trees, and obtain pictures of the regions which are successively filled in by the Peano curve of Cannon and Thurston.

- Warren Dicks, Peter A. Linnell
- 2005

We determine the L 2-Betti numbers of all one-relator groups and all surface plus one relation groups. We also obtain some information about the L 2-cohomology of left-orderable groups, and deduce the non-L 2 result that, in any left-orderable group of homological dimension one, all two-generator subgroups are free. 1 Notation and background Let G be a… (More)

- Warren Dicks, Peter H. Kropholler, Ian J. Leary
- 2008

For each finite ordinal n, and each locally-finite group G of cardinality ℵ n , we construct an (n + 1)-dimensional, contractible CW-complex on which G acts with finite stabilizers. We use the complex to obtain information about cohomology with induced coefficients. Our techniques also give information about the location of some large free abelian groups in… (More)

- IGOR MINEYEV, Hanna Neumann, Walter Neumann, Warren Dicks, Ivan Mineyev
- 2012

Submultiplicativity, an analytic property generalizing the Strengthened Hanna Neumann Conjecture (SHNC) to complexes was proved in [2] assuming the deep-fall property. This in particular implied SHNC. The purpose of this note is to write the proof of the original SHNC and purely in terms of groups and graphs. We also give explicit examples showing that the… (More)

- Warren Dicks
- 2008

Let G be a group, let T be an (oriented) G-tree with finite edge stabilizers, and let V T denote the vertex set of T. We show that, for each G-retract V ′ of the G-set V T , there exists a G-tree whose edge stabilizers are finite and whose vertex set is V ′. This fact leads to various new consequences of the almost stability theorem. We also give an example… (More)

- Pere Ara, Warren Dicks, Desmond Sheiham
- 2006

Let R be a ring, let F be a free group, and let X be a basis of F. Let : RF → R denote the usual augmentation map for the group ring RF , let X∂ := {x − 1 | x ∈ X} ⊆ RF , let Σ denote the set of matrices over RF that are sent to invertible matrices by , and let (RF)Σ −1 denote the universal localization of RF at Σ. A classic result of Magnus and Fox gives… (More)