English

Dehn filling and the Thurston norm

Geometric Topology 2016-08-09 v1

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.

Keywords

Cite

@article{arxiv.1608.02443,
  title  = {Dehn filling and the Thurston norm},
  author = {Kenneth L. Baker and Scott A. Taylor},
  journal= {arXiv preprint arXiv:1608.02443},
  year   = {2016}
}