Dehn filling and the Thurston norm

Kenneth L. Baker; Scott A. Taylor

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arXiv · 1608.02443

Dehn filling and the Thurston norm

Kenneth L. Baker·Scott A. Taylor

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Abstract

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.

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BibTeX RIS

Kenneth L. Baker, Scott A. Taylor. 2016-08-08. Dehn filling and the Thurston norm. https://arxiv.org/abs/1608.02443

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