Small knots of large Heegaard genus

William Worden

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arXiv · 1907.06820

Small knots of large Heegaard genus

William Worden

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Abstract

Building off ideas developed by Agol, we construct a family of hyperbolic knots $K_n$ whose complements contain no closed incompressible surfaces and have Heegaard genus exactly $n$. These are the first known examples of small knots having large Heegaard genus. Using work of Futer and Purcell, we are able to bound the crossing number for each $K_n$ in terms of $n$.

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William Worden. 2020-10-08. Small knots of large Heegaard genus. https://arxiv.org/abs/1907.06820

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