Conjugacy in Thompson’s Group F
نویسنده
چکیده
We complete the program begun by Brin and Squier of characterising conjugacy in Thompson’s group F using the standard action of F as a group of piecewise linear homeomorphisms of the unit interval.
منابع مشابه
The Conjugacy Problem in Extensions of Thompson’s Group F
We solve the twisted conjugacy problem on Thompson’s group F . We also exhibit orbit undecidable subgroups of Aut(F ), and give a proof that Aut(F ) and Aut+(F ) are orbit decidable provided a certain conjecture on Thompson’s group T is true. By using general criteria introduced by Bogopolski, Martino and Ventura in [5], we construct a family of free extensions of F where the conjugacy problem ...
متن کاملConjugacy in Thompson’s Group
We present a characterisation of conjugacy in Thompson’s group using the natural action of F on the interval [0, 1]. This characterisation completes the program begun by Brin and Squier [BS01]. Our characterisation also provides another solution to the conjugacy problem in Thompson’s group which was first solved by Guba and Sapir using diagram groups [GS97]. A number of other solutions exist du...
متن کاملThe 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...
متن کاملConjugacy in Thompson’s groups
We give a unified solution the conjugacy problem in Thompson’s groups F , V , and T using strand diagrams, a modification of tree diagrams. We then analyze the complexity of the resulting algorithms. Thompson’s group F is the group of all piecewise-linear homeomorphisms of the unit interval satisfying the following conditions: 1. Every slope is a power of two, and 2. Every breakpoint has dyadic...
متن کاملar X iv : 0 71 0 . 36 33 v 2 [ m at h . G R ] 1 4 N ov 2 00 8 Dynamics in Thompson ’ s group F
We describe an explicit relationship between strand diagrams and piecewiselinear functions for elements of Thompson’s group F . Using this correspondence, we investigate the dynamics of elements of F , and we show that conjugacy of one-bump functions can be described by a Mather-type invariant. Thompson’s group F is the group of all piecewise-linear homeomorphisms of the unit interval with fini...
متن کامل