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July 2019 Dehn filling and the Thurston norm
Kenneth L. Baker, Scott A. Taylor
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J. Differential Geom. 112(3): 391-409 (July 2019). DOI: 10.4310/jdg/1563242469


For a compact, orientable, irreducible $3$-manifold with toroidal boundary that is not the product of a torus and an interval or a cable space, each boundary torus has a finite set of slopes such that, if avoided, the Thurston norm of a Dehn filling behaves predictably. More precisely, for all but finitely many slopes, the Thurston norm of a class in the second homology of the filled manifold plus the so-called winding norm of the class will be equal to the Thurston norm of the corresponding class in the second homology of the unfilled manifold. This generalizes a result of Sela and is used to answer a question of Baker–Motegi concerning the Seifert genus of knots obtained by twisting a given initial knot along an unknot which links it.

Funding Statement

KLB was partially supported by a grant from the Simons Foundation (#209184 to Kenneth L. Baker). SAT was supported by a grant from the Natural Science Division of Colby College.


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Kenneth L. Baker. Scott A. Taylor. "Dehn filling and the Thurston norm." J. Differential Geom. 112 (3) 391 - 409, July 2019.


Received: 12 August 2016; Published: July 2019
First available in Project Euclid: 16 July 2019

zbMATH: 07088290
MathSciNet: MR3981293
Digital Object Identifier: 10.4310/jdg/1563242469

Rights: Copyright © 2019 Lehigh University


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Vol.112 • No. 3 • July 2019
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