Tame combing and almost convexity conditions

Details Tame combing and almost convexity conditions Tame combing and almost convexity conditions

2009-09-01

arxiv.org/abs/0909.0279v2

Mathematics

Group Theory

36 pages, 9 figures

Scientific paper

We give the first examples of groups which admit a tame combing with linear radial tameness function with respect to any choice of finite presentation, but which are not minimally almost convex on a standard generating set. Namely, we explicitly construct such combings for Thompson's group F and the Baumslag-Solitar groups BS(1, p) with p \ge 3. In order to make this construction for Thompson's group F, we significantly expand the understanding of the Cayley complex of this group with respect to the standard finite presentation. In particular we describe a quasigeodesic set of normal forms and combinatorially classify the arrangements of 2-cells adjacent to edges that do not lie on normal form paths.

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