The simultaneous conjugacy problem in groups of piecewise linear functions

Details The simultaneous conjugacy problem in groups of piecewise linear functions The simultaneous conjugacy problem in groups of piecewise linear functions

2006-07-06

arxiv.org/abs/math/0607167v3

Mathematics

Group Theory

33 pages, 7 figures; final version; to appear in "Groups, Geometry and Dynamics"

Scientific paper

Guba and Sapir asked if the simultaneous conjugacy problem was 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.

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