Corpus ID: 9764857

Thompson's group F(n) is not minimally almost convex

@inproceedings{Wladis2007ThompsonsGF,
  title={Thompson's group F(n) is not minimally almost convex},
  author={Claire Wladis},
  year={2007}
}
We prove that Thompson's group F (n) is not minimally almost convex with respect to the standard finite generating set. A group G with Cayley graph Γ is not minimally almost convex if for arbitrarily large values of m there exist elements g,h ∈ Bm such that dΓ(g,h )=2a nddBm (g,h )=2 m. (Here Bm is the ball of radius m centered at the identity.) We use tree-pair diagrams to represent elements of F (n) and then use Fordham's metric to calculate geodesic length of elements of F (n). Cleary and… Expand
Unusual Geodesics in generalizations of Thompson's Group F
We prove that seesaw words exist in Thompson's Group F(N) for N=2,3,4,... with respect to the standard finite generating set X. A seesaw word w with swing k has only geodesic representatives endingExpand
THOMPSON'S GROUP IS DISTORTED IN THE THOMPSON-STEIN GROUPS
We show that the inclusion map of the generalized Thompson groups F(n i ) is exponentially distorted in the Thompson―Stein groups F(n 1 , ... , n k ) for k > 1. One consequence is that F isExpand
The word problem and the metric for the Thompson-Stein groups
  • Claire Wladis
  • Mathematics, Computer Science
  • J. Lond. Math. Soc.
  • 2012
TLDR
A unique normal form for elements of F(n1, ..., nk) (with respect to the standard infinite generating set developed by Melanie Stein) is introduced which provides a solution to the word problem. Expand
Tree-pair Diagrams, the Word Problem, and the Metric for Generalizations of Thompson's Group F on more than One Integer
We consider the Thompson-Stein group F(n_1,...,n_k) for integers n_1,...,n_k and k greater than 1. We highlight several differences between the cases k=1$ and k>1, including the fact that minimalExpand

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Thompson's group F is maximally nonconvex
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