The Simultaneous Conjugacy Problem in Groups of Piecewise Linear Functions
نویسندگان
چکیده
Guba and Sapir asked, in their joint paper [8], if the simultaneous conjugacy problem was solvable in Diagram Groups or, at least, for Thompson’s group F . We give an elementary proof for the solution of the latter question. This relies purely on the description of F as the group of piecewise linear orientation-preserving homeomorphisms of the unit. The techniques we develop allow us also to solve the ordinary conjugacy problem as well, and we can compute roots and centralizers. Moreover, these techniques can be generalized to solve the same questions in larger groups of piecewise-linear homeomorphisms.
منابع مشابه
The Simultaneous Conjugacy Problem in Thompson’s Group F
Guba and Sapir asked, in their joint paper [3], if the simultaneous conjugacy problem was solvable in Diagram Groups or, at least, for Thompson’s group F . We give an elementary proof for the solution of the latter question. This relies purely on the description of F as the group of piecewise linear orientationpreserving homeomorphisms of the unit interval with dyadic breakpoints and slopes tha...
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