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 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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 391-409 |
| Number of pages | 19 |
| Journal | Journal of Differential Geometry |
| Volume | 112 |
| Issue number | 3 |
| DOIs | |
| State | Published - Jan 1 2019 |
| Externally published | Yes |
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ASJC Scopus subject areas
- Analysis
- Algebra and Number Theory
- Geometry and Topology
Cite this
Dehn filling and the thurston norm. / Baker, Kenneth L.; Taylor, Scott A.
In: Journal of Differential Geometry, Vol. 112, No. 3, 01.01.2019, p. 391-409.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Dehn filling and the thurston norm
AU - Baker, Kenneth L.
AU - Taylor, Scott A.
PY - 2019/1/1
Y1 - 2019/1/1
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.
UR - http://www.scopus.com/inward/record.url?scp=85072626608&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85072626608&partnerID=8YFLogxK
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 -