Warren Dicks

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Recently, M. Bestvina and N. Brady have exhibited groups that are of type FP 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)
We use elementary methods to compute the L-dimension of the eigenspaces 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 lamplighter group found by Grigorchuk-Zuk [4]. The latter result was used by(More)
We determine the L-Betti numbers of all one-relator groups and all surface-plus-one-relation groups. We also obtain some information about the L -cohomology of left-orderable groups, and deduce the non-L result that, in any left-orderable group of homological dimension one, all two-generator subgroups are free. 2000 Mathematics Subject Classification.(More)
1.1 Notation. Let rank(G) denote the smallest cardinal κ such that there exists some set of generators of G of cardinality κ. If G is not finitely generated, then rank(G) = |G|, and we define א-rank(G) to be the ordinal α such that rank(G) = אα; ifG is finitely generated, then rank(G) < |G|, and we set א-rank(G) = −1. Recall that, for each ordinal α, ωα(More)
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)
This article surveys many standard results about the braid group, with emphasis on simplifying the usual algebraic proofs. We use van der Waerden’s trick to illuminate the Artin-Magnus proof of the classic presentation of the braid group considered as the algebraic mapping-class group of a disc with punctures. We give a simple, new proof of the(More)
To each once-punctured-torus bundle, Tφ, over the circle with pseudo-Anosov monodromy φ, there are associated two tessellations of the complex plane: one, ∆(φ), is (the projection from ∞ of) the triangulation of a horosphere at ∞ induced by the canonical decomposition into ideal tetrahedra, and the other, CW (φ), is a fractal tessellation given by the(More)