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.

arXiv comment72 pages, 17 figures; v2, minor revision, corrected the proof of Lemma 6.22, accepted for publication at Inventiones mathematicae

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Cited by in corpus (5)

• The full spectrum of scl on recursively presented groups
• Spectral gap of scl in graphs of groups and $3$-manifolds
• The Minimal Genus of Homology Classes in a Finite 2-Complex
• Algebraic irrational stable commutator length in finitely presented groups
• On stable commutator length of non-filling curves in surfaces