# THOMPSON'S GROUP F

@article{Belk2004THOMPSONSGF, title={THOMPSON'S GROUP F}, author={James M. Belk}, journal={arXiv: Group Theory}, year={2004} }

We introduce forest diagrams and strand diagrams for elements of Thompson's group F. A forest diagram is a pair of infinite, bounded binary forests together with an order-preserving bijection of the leaves. Using forest diagrams, we derive a simple length formula for elements of F, and we discuss applications to the geometry of the Cayley graph, including a new upper bound on the isoperimetric constant (a.k.a. Cheeger constant) of F. Strand diagrams are similar to tree diagrams, but they can be… Expand

#### 78 Citations

Conjugacy in Thompson's Groups

- Mathematics
- 2007

We give a unified solution the conjugacy problem in Thompson’s groups F , V , and T using strand diagrams, a modification of tree diagrams. We then analyze the complexity of the resulting algorithms.… Expand

DYNAMICS IN THOMPSON’S GROUP F

- 2008

We describe an explicit relationship between strand diagrams and piecewise-linear functions for elements of Thompson’s group F . Using this correspondence, we investigate the dynamics of elements of… Expand

On Belk's classifying space for Thompson's group F

- Mathematics
- 2013

The space of configurations of n ordered points in the plane serves as a classifying space for the pure braid group PB_n. Elements of Thompson's group F admit a model similar to braids, except… Expand

Finiteness Properties of the Braided Thompson's Groups and the Brin-Thompson Groups

- Philosophy
- 2015

A group G is of type Fn if there is a K(G, 1) complex that has finite n-skeleton. It is of type F∞, if it is of type Fn for all n ∈ N. Here the property F1 is equivalent to G being finitely generated… Expand

Some Graphs Related to Thompson’s Group F

- Mathematics
- 2010

The Schreier graphs of Thompson’s group F with respect to the stabilizer of 1/2 and generators x 0 and x 1 , and of its unitary representation in L 2 ([0, 1]) induced by the standard action on the… Expand

Jones Representations of Thompson’s Group F Arising from Temperley–Lieb–Jones Algebras

- Mathematics
- International Mathematics Research Notices
- 2019

Following a procedure due to Jones, using suitably normalized elements in a Temperley–Lieb–Jones (planar) algebra, we introduce a 3-parametric family of unitary representations of the Thompson’s… Expand

Pure braid subgroups of braided Thompson's groups

- Mathematics
- 2006

We describe some properties of braided generalizations of Thompson's groups, introduced by Brin and Dehornoy. We give slightly different characterizations of the braided Thompson's groups $BV$ and… Expand

Çark Groupoids and Thompson’s Groups

- 2016

In this work, we introduce a groupoid, called the class groupoid and denoted by C G , which generalizes the Ptolemy groupoid constructions of Penner both in the finite case, i.e. for surfaces of… Expand

Tamari lattices, forests and Thompson monoids

- Computer Science, Mathematics
- Eur. J. Comb.
- 2007

A connection relating Tamari lattices on symmetric groups regarded as lattices under the weak Bruhat order to the positive monoid P of Thompson group F is presented. Tamari congruence classes… Expand

Algorithms and classification in groups of piecewise-linear homeomorphisms

- Mathematics
- 2008

The first part (Chapters 2 through 5) studies decision problems in Thompson's groups F, T, V and some generalizations. The simultaneous conjugacy problem is determined to be solvable for Thompson's… Expand

#### References

SHOWING 1-10 OF 38 REFERENCES

Forest Diagrams for Elements of Thompson's Group F

- Mathematics, Computer Science
- Int. J. Algebra Comput.
- 2005

We introduce forest diagrams to represent elements of Thompson's group F. These diagrams relate to a certain action of F on the real line in the same way that tree diagrams relate to the standard… Expand

Combinatorial properties of Thompson's group F

- Mathematics
- 2002

We study some combinatorial consequences of Blake Fordham's theorems on the word metric of Thompson's group F in the standard two generator presentation. We explore connections between the tree pair… Expand

Minimal Length Elements of Thompson's Group F

- Mathematics
- 2003

Elements of the group are represented by pairs of binary trees and the structure of the trees gives insight into the properties of the elements of the group. The review section presents this… Expand

On the Properties of The Cayley Graph of Richard Thompson's Group F

- Mathematics, Computer Science
- Int. J. Algebra Comput.
- 2004

The growth rate of F, R. Thompson's group F in generators x0, x1, has a lower bound of . Expand

Thompson's group F is not almost convex

- Mathematics
- 2002

Abstract We show that Thompson's group F does not satisfy Cannon's almost convexity condition AC ( n ) for any positive integer n with respect to the standard generating set with two elements. To… Expand

Growth of Positive Words in Thompson's Group F

- Mathematics
- 2004

Abstract Although it is well known that the growth of Thompson's group F is exponential, the exact growth function is still unknown. Elements of its submonoid of positive words can be described using… Expand

The algebraic theory of semigroups

- Mathematics
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This book, along with volume I, which appeared previously, presents a survey of the structure and representation theory of semi groups. Volume II goes more deeply than was possible in volume I into… Expand

Semigroups, Rings, and Markov Chains

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- 2000

We analyze random walks on a class of semigroups called “left-regular bands.” These walks include the hyperplane chamber walks of Bidigare, Hanlon, and Rockmore. Using methods of ring theory, we show… Expand

Splitting homotopy idempotents II

- Mathematics
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Let A be an abelian category with enough projectives and let ℋ be the quotient category of A obtained by identifying with zero all maps which factor through projectives. ℋ is the Eckmann-Hilton… Expand

Almost convex groups and the eight geometries

- Mathematics
- 1993

IfM is a closed Nil geometry 3-manifold then π1(M) is almost convex with respect to a fairly simple “geometric” generating set. IfG is a central extension or a ℤ extension of a word hyperbolic group,… Expand