Linear Bounds of the Crosscap Number of Knots

2023/08/17 by McConkey, Rob
#FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2308.09159

Abstract

Kalfagianni and Lee found two-sided bounds for the crosscap number of an alternating link in terms of certain coefficients of the Jones polynomial. We show here that we can find similar two-sided bounds for the crosscap number of Conway sums of strongly alternating tangles. Then we find families of links for which these coefficients of the Jones polynomial and the crosscap number grow independently. These families will enable us to show that neither linear bound generalizes for all links.

Related

• Automatic computation of crosscap number of alternating knots
• Average crosscap number of a 2-bridge knot
• Bounds on the Crosscap Number of Torus Knots
• Crosscap numbers of alternating links via state codes
• Non-triviality of the Jones polynomial and the crossing numbers of amphicheiral knots