Seifert Klein bottles for knots with common boundary slopes
| dc.creator | Valdez-Sanchez, Luis G. | |
| dc.date | 2004-09-23 | |
| dc.date | 2004-09-25 | |
| dc.date.accessioned | 2026-07-07T05:12:31Z | |
| dc.date.available | 2026-07-07T05:12:31Z | |
| dc.description | We consider the question of how many essential Seifert Klein bottles with common boundary slope a knot in S^3 can bound, up to ambient isotopy. We prove that any hyperbolic knot in S^3 bounds at most six Seifert Klein bottles with a given boundary slope. The Seifert Klein bottles in a minimal projection of hyperbolic pretzel knots of length 3 are shown to be unique and pi_1-injective, with surgery along their boundary slope producing irreducible toroidal manifolds. The cable knots which bound essential Seifert Klein bottles are classified; their Seifert Klein bottles are shown to be non-pi_1-injective, and unique in the case of torus knots. For satellite knots we show that, in general, there is no upper bound for the number of distinct Seifert Klein bottles a knot can bound. | |
| dc.description | Published by Geometry and Topology Monographs at http://www.maths.warwick.ac.uk/gt/GTMon7/paper2.abs.html | |
| dc.identifier | https://arxiv.org/abs/math/0409459 | |
| dc.identifier | http://arxiv.org/abs/math/0409459 | |
| dc.identifier | Geom. Topol. Monogr. 7 (2004) 27-68 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/72604 | |
| dc.subject | Geometric Topology | |
| dc.subject | 57M25, 57N10 | |
| dc.title | Seifert Klein bottles for knots with common boundary slopes | |
| dc.type | text |