Topology & Geometric Group Theory Seminar

Spring 2008

1:30 - 2:30, Malott 207

Tuesday, February 5

Danny Calegari, Caltech

Stable commutator length is rational in free groups

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.

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