On two crossing numbers of algebraic knots under Hopf fibration

Maciej Mroczkowski

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arXiv · 2006.16123

On two crossing numbers of algebraic knots under Hopf fibration

Maciej Mroczkowski

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Abstract

We answer a question posed by Fielder in [1] concerning two notions of crossing number for algebraic knots $K$ under Hopf fibration, one topological, denoted $h(K)$, the other coming from the realization of such knots around complex singularities, denoted $C_{alg}(K)$. We show that $C_{alg}(K)-h(K)$ can be arbitrarily large. We also give an upper bound for $h$ of some families of knots such as torus knots $T(2,n)$, twist knots and their mirror images.

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BibTeX RIS

Maciej Mroczkowski. 2020-06-29. On two crossing numbers of algebraic knots under Hopf fibration. https://arxiv.org/abs/2006.16123

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