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.
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Acknowledgements
I would like to thank Danny Calegari for his consistent encouragements and guidance. I also thank Matt Clay, Max Forester, Joel Louwsma and Tim Susse for helpful conversations on their related studies. Finally I would like to thank Benson Farb, Martin Kassabov, Jason Manning, and Alden Walker for useful discussions, and thank the anonymous referee for good suggestions improving the paper.
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