The Neuwirth conjecture for knots
Let be a non-trivial knot in .
Neuwirth conjecture. There exists a closed surface such that contains non-separatingly and is essential in the exterior of .
The conjecture is known for alternating, generalized alternating, Montesinos, and several other classes of knots, but remains open in general.
References
Primary source
Makoto Ozawa, “Knots and surfaces”, arXiv:1603.09039 (2017).
Additional references
3 papers in this index state this conjecture (2011–2016). The statement above is taken from the most recent of them; the others are arXiv:1211.5941, arXiv:1103.2576.
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