Small knots of large Heegaard genus

William Worden

Small knots of large Heegaard genus

Geometric Topology 2020-10-09 v3

Authors: William Worden

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 $n$ .

Keywords

hyperbolic knots heegaard genus small knots incompressible surfaces crossing number

Cite

@article{arxiv.1907.06820,
  title  = {Small knots of large Heegaard genus},
  author = {William Worden},
  journal= {arXiv preprint arXiv:1907.06820},
  year   = {2020}
}

Comments

Final version to appear in Communications in Analysis and Geometry. Mostly minor changes/corrections, proof of Lemma 5.3 expanded for clarity and some errors corrected. 18 pages, 10 figures

Small knots of large Heegaard genus

Abstract

Keywords

Cite

Comments

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