We show that the free group of rank 2 is a limit of 2-markings of Thompson’s group F in the space of all 2-marked groups. More specifically, we find a sequence of generating pairs for F so that as one goes out the sequence, the length of the shortest relation satisfied by the generating pair goes to infinity.
Cite this article
Matthew G. Brin, The free group of rank 2 is a limit of Thompson’s group <var>F</var>. Groups Geom. Dyn. 4 (2010), no. 3, pp. 433–454DOI 10.4171/GGD/90