On 3-super bridge knots

2012/09/14 by Rama Mishra, Mishra, Rama
Mathematics · #57M25 (Primary) 14P25 (Secondary) #FOS: Mathematics #Geometric Topology (math.GT) #math.GT #msc:14P25 #msc:57M25

paper · pdf · doi:10.48550/arxiv.1209.3119

11 pages, 7 figures

arxiv created 2012/09/14 · arxiv updated 2012/09/17

Abstract

It is known that there are only finitely many knots with super bridge index 3. Jin and Jeon have provided a list of possible such candidates. However, they conjectured that the only knots with super bridge index 3 are trefoil and the figure eight knot. In this paper, we prove that the 5₂ knot and the 6₂ knot are also 3-super bridge knots by providing a polynomial representation of these knots in degree 6. This also answers a question asked by Durfee and O'Shea in their paper on polynomial knots: is there any 5-crossing knot in degree 6?

Related

• Spaces of polynomial knots in low degree
• The lexicographic degree of the first two-bridge knots
• Superbridge and Bridge Indices for Knots
• The 2-bridge knots of up to 16 crossings
• There are only finitely many 3-superbridge knots