TY - JOUR
T1 - Dehn filling and the thurston norm
AU - Baker, Kenneth L.
AU - Taylor, Scott A.
N1 - Funding Information:
∗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. Received August 12, 2016.
Publisher Copyright:
© 2019 International Press of Boston, Inc.. All rights reserved.
Copyright:
Copyright 2019 Elsevier B.V., All rights reserved.
PY - 2019
Y1 - 2019
N2 - 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 man-ifold plus the so-called winding norm of the class will be equal to the Thurston norm of the corresponding class in the second ho-mology 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.
AB - 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 man-ifold plus the so-called winding norm of the class will be equal to the Thurston norm of the corresponding class in the second ho-mology 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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U2 - 10.4310/jdg/1563242469
DO - 10.4310/jdg/1563242469
M3 - Article
AN - SCOPUS:85072626608
VL - 112
SP - 391
EP - 409
JO - Journal of Differential Geometry
JF - Journal of Differential Geometry
SN - 0022-040X
IS - 3
ER -