Research ArticleNo Access

Families of curly knots

C. Ernst

https://orcid.org/0000-0002-2334-6229

Department of Mathematics, Western Kentucky University, Bowling Green, KY 42101, USA

E-mail Address: claus.ernst@wku.edu

Corresponding author.

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and

S. Gover

Department of Mathematics, Western Kentucky University, Bowling Green, KY 42101, USA

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https://doi.org/10.1142/S0218216522501012Cited by:0 (Source: Crossref)

Abstract

A spiral knot or link diagram (introduced in [C. Adams, R. Hudson, R. Morrison, W. George, L. Starkston, S. Taylor and O. Turanova, The spiral index of knots, Math. Proc. Cambridge Philos. Soc. 149(2) (2010) 297–315]) is an oriented knot or link diagram where, when traversing through the planar diagram, the curvature does not change sign. An oriented knot or link type is called curly if it admits a spiral diagram with fewer maxima than the braid index of that knot or link type. In this paper, we exhibit families of curly knots and links.

Keywords:

AMSC: 57K10

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