Groups, Geometry, and Dynamics


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Volume 4, Issue 3, 2010, pp. 433–454
DOI: 10.4171/GGD/90

Published online: 2010-06-16

The free group of rank 2 is a limit of Thompson’s group F

Matthew G. Brin[1]

(1) SUNY Binghamton University, USA

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.

Keywords: Thompson’s group, limit of marked groups

Brin Matthew: The free group of rank 2 is a limit of Thompson’s group F. Groups Geom. Dyn. 4 (2010), 433-454. doi: 10.4171/GGD/90