Stable commutator length is rational in free groups
by
Danny Calegari
Caltech

1. For any group, there is a natural (pseudo)-norm on the vector space B1 of real (group) 1-boundaries, called the stable commutator length norm, which generalizes stable commutator length on elements of the commutator subgroup. We show that in a free group, the unit ball of this pseudo-norm, restricted to any finite dimensional rational subspace of B1, is a finite sided rational polyhedron. As a corollary, we show that every element of a free group has rational stable commutator length, and moreover every element of the commutator subgroup rationally bounds an injective map of a surface group into the free group. This talk will be accessible to graduate students.

Date received: January 24, 2008

Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cawj-10.