Geodesic
The simultaneous conjugacy problem in groups of piecewise linear functions
Martin Kassabov1 orcid ; Francesco Matucci2 orcid
1Cornell University, Ithaca, United States
2Université Paris-Sud, Orsay, France
Groups, geometry, and dynamics, Tome 6 (2012) no. 2, pp. 279-315

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DOI

Guba and Sapir asked if the simultaneous conjugacy problem is solvable in diagram groups or, at least, for Thompson’s group F. We give a solution to the latter question using elementary techniques which rely purely on the description of F as the group of piecewise linear orientation-preserving homeomorphisms of the unit interval. The techniques we develop extend the ones used by Brin and Squier allowing us to compute roots and centralizers as well. Moreover, these techniques can be generalized to solve the same question in larger groups of piecewise-linear homeomorphisms.
DOI : 10.4171/ggd/158
Classification : 20-XX, 37-XX, 00-XX
Mots-clés : Conjugacy problem, Thompson’s groups

Martin Kassabov  1   ; Francesco Matucci  2

1 Cornell University, Ithaca, United States
2 Université Paris-Sud, Orsay, France 
Martin Kassabov; Francesco Matucci. The simultaneous conjugacy problem in groups  of piecewise linear functions. Groups, geometry, and dynamics, Tome 6 (2012) no. 2, pp. 279-315. doi: 10.4171/ggd/158
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