Seifert Klein bottles for knots with common boundary slopes

dc.creatorValdez-Sanchez, Luis G.
dc.date2004-09-23
dc.date2004-09-25
dc.date.accessioned2026-07-07T05:12:31Z
dc.date.available2026-07-07T05:12:31Z
dc.descriptionWe 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.descriptionPublished by Geometry and Topology Monographs at http://www.maths.warwick.ac.uk/gt/GTMon7/paper2.abs.html
dc.identifierhttps://arxiv.org/abs/math/0409459
dc.identifierhttp://arxiv.org/abs/math/0409459
dc.identifierGeom. Topol. Monogr. 7 (2004) 27-68
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/72604
dc.subjectGeometric Topology
dc.subject57M25, 57N10
dc.titleSeifert Klein bottles for knots with common boundary slopes
dc.typetext

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