# Conjugacy and dynamics in Thompson’s groups

@article{Belk2007ConjugacyAD, title={Conjugacy and dynamics in Thompson’s groups}, author={James M. Belk and Francesco Matucci}, journal={Geometriae Dedicata}, year={2007}, volume={169}, pages={239-261} }

We give a unified solution to the conjugacy problem for Thompson’s groups $$F, \,T$$F,T, and $$V$$V. The solution uses “strand diagrams”, which are similar in spirit to braids and generalize tree-pair diagrams for elements of Thompson’s groups. Strand diagrams are closely related to piecewise-linear functions for elements of Thompson’s groups, and we use this correspondence to investigate the dynamics of elements of $$F$$F. Though many of the results in this paper are known, our approach is new… Expand

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#### 40 Citations

An Implementation of the Solution to the Conjugacy Problem on Thompson's Group V

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We describe an implementation of the solution to the conjugacy problem in Thompson’s group V as presented by James Belk and Francesco Matucci in 2013. Thompson’s group V is an infinite finitely… Expand

Deciding Conjugacy in Thompson's Group F in Linear Time

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- 2013 15th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing
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It is proved that the solution to the conjugacy problem in Thompson's group F theoretically achieves a linear time bound in the size of the input, and the algorithm is presented a quadratic time working solution. Expand

The conjugacy problem in extensions of Thompson’s group F

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In this paper we generalize techniques of Belk-Matucci to solve the conjugacy problem for every Thompson-like group $V_n(H)$, where $n \geq 2$ and $H$ is a subgroup of the symmetric group on $n$… Expand

The power conjugacy problem in Higman-Thompson groups

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- Int. J. Algebra Comput.
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An introduction to the universal algebra approach to Higman–Thompson groups (including Thompson’s group V) is given, following a series of lectures by Graham Higman in 1973, and an algorithm for the power conjugacy problem in these groups is constructed. Expand

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Adviser: Professor Mark Brittenham We study Richard Thompson's group V , and some generalizations of this group. V was one of the first two examples of a finitely presented, infinite, simple group.… Expand

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

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Röver's Simple Group Is of Type $F_\infty$

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We prove that Claas R\"over's Thompson-Grigorchuk simple group $V\mathcal{G}$ has type $F_\infty$. The proof involves constructing two complexes on which $V\mathcal{G}$ acts: a simplicial complex… Expand

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