Dehn filling and the thurston norm

Kenneth L. Baker, Scott A. Taylor

Research output: Contribution to journalArticle

1 Citation (Scopus)

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 languageEnglish (US)
Pages (from-to)391-409
Number of pages19
JournalJournal of Differential Geometry
Volume112
Issue number3
DOIs
StatePublished - Jan 1 2019
Externally publishedYes

Fingerprint

Dehn Filling
Norm
Knot
Slope
Torus
Unknot
Manifolds with Boundary
Cable
Homology
Finite Set
Genus
Generalise
Interval
Class

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 journalArticle

Baker, Kenneth L. ; Taylor, Scott A. / Dehn filling and the thurston norm. In: Journal of Differential Geometry. 2019 ; Vol. 112, No. 3. pp. 391-409.
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