Seifert Klein bottles for knots with common boundary slopes

@article{ValdezSnchez2004SeifertKB,
  title={Seifert Klein bottles for knots with common boundary slopes},
  author={Luis G. Valdez-S{\'a}nchez},
  journal={arXiv: Geometric Topology},
  year={2004}
}
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… 

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