The conjugacy problem in extensions of Thompson's group F
Group Theory
2013-09-10 v2
Abstract
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 is unsolvable. As a byproduct of our techniques, we give a new proof of a result of Bleak-Fel'shtyn-Goncalves in [4] showing that F has property R_\infty, and which can be extended to show that Thompson's group T also has property R_\infty.
Keywords
Cite
@article{arxiv.1307.6750,
title = {The conjugacy problem in extensions of Thompson's group F},
author = {José Burillo and Francesco Matucci and Enric Ventura},
journal= {arXiv preprint arXiv:1307.6750},
year = {2013}
}
Comments
31 pages, 2 figures; improved exposition