The conjugacy problem in extensions of Thompson’s group F - Burillo, José; Matucci, Francesco; Ventura, Enric (Israel journal of mathematics, 2016)
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–Gonçalves in [4] showing that F has property R ∞ , and which can be extended to show that Thompson’s group T also has property R ∞ .