Cusp types of quotients of hyperbolic knot complements

Neil R Hoffman

Cusp types of quotients of hyperbolic knot complements

Geometric Topology 2022-09-21 v3

Authors: Neil R Hoffman

Abstract

This paper completes a classification of the types of orientable and non-orientable cusps that can arise in the quotients of hyperbolic knot complements. In particular, $S^2(2,4,4)$ cannot be the cusp cross-section of any orbifold quotient of a hyperbolic knot complement. Furthermore, if a knot complement covers an orbifold with a $S^2(2,3,6)$ cusp, it also covers an orbifold with a $S^2(3,3,3)$ cusp. We end with a discussion that shows all cusp types arise in the quotients of link complements.

Keywords

hyperbolic knot complements orbifold quotients cusp types cusp cross-sections link complements classification

Cite

@article{arxiv.2001.05066,
  title  = {Cusp types of quotients of hyperbolic knot complements},
  author = {Neil R Hoffman},
  journal= {arXiv preprint arXiv:2001.05066},
  year   = {2022}
}

Comments

13 pages, 6 figures, updates include a complete classification of the cusp types that can show up in the quotients of link complements

Cusp types of quotients of hyperbolic knot complements

Abstract

Keywords

Cite

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