On the Neuwirth conjecture for knots

  title={On the Neuwirth conjecture for knots},
  author={Makoto Ozawa and J. Hyam Rubinstein},
  journal={arXiv: Geometric Topology},
Neuwirth asked if any non-trivial knot in the 3-sphere can be embedded in a closed surface so that the complement of the surface is a connected essential surface for the knot complement. In this paper, we examine some variations on this question and prove it for all knots up to 11 crossings except for two examples. We also establish the conjecture for all Montesinos knots and for all generalized arborescently alternating knots. For knot exteriors containing closed incompressible surfaces… 

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