Guba and Sapir asked if the simultaneous conjugacy problem is solvable in diagram groups or, at least, for Thompson’s group . We give a solution to the latter question using elementary techniques which rely purely on the description of 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.
Cite this article
Martin Kassabov, Francesco Matucci, The simultaneous conjugacy problem in groups of piecewise linear functions. Groups Geom. Dyn. 6 (2012), no. 2, pp. 279–315DOI 10.4171/GGD/158