JournalsggdVol. 6, No. 2pp. 279–315

The simultaneous conjugacy problem in groups of piecewise linear functions

  • Martin Kassabov

    Cornell University, Ithaca, United States
  • Francesco Matucci

    Université Paris-Sud, Orsay, France
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Abstract

Guba and Sapir asked if the simultaneous conjugacy problem is solvable in diagram groups or, at least, for Thompson’s group FF. We give a solution to the latter question using elementary techniques which rely purely on the description of FF 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.

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Martin Kassabov, Francesco Matucci, The simultaneous conjugacy problem in groups of piecewise linear functions. Groups Geom. Dyn. 6 (2012), no. 2, pp. 279–315

DOI 10.4171/GGD/158