Let G = * λ G λ be a free product of torsion-free groups, and let g ∈ [G, G] be any element not conjugate into a G λ . Then scl G (g) ≥ 1/2. This generalizes, and gives a new proof of a theorem of Duncan-Howie [10].
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.
57M07; 20E06, 20F65
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