Scl in graphs of groups

Abstract

Let G be a group acting on a tree with cyclic edge and vertex stabilizers. Then stable commutator length (scl) is rational in G. Furthermore, scl varies predictably and converges to rational limits in so-called "surgery" families. This is a homological analog of the phenomenon of geometric convergence in hyperbolic Dehn surgery.

72 pages, 17 figures; v2, minor revision, corrected the proof of Lemma 6.22, accepted for publication at Inventiones mathematicae