Bounds on the Crosscap Number of Torus Knots

2004/09/29 by Thomas W. Mattman, Mattman, Thomas W., Owen Sizemore +1
Mathematics · #57M25 #FOS: Mathematics #Geometric Topology (math.GT) #math.GT #msc:57M25

paper · pdf · doi:10.48550/arxiv.math/0409581

7 Pages, 0 figures Version 2 - corrected a typo: Clark showed c(K) \le 2g(K) + 1

arxiv created 2004/10/04 · arxiv updated 2009/12/01

Abstract

For a torus knot K, we bound the crosscap number c(K) in terms of the genus g(K) and crossing number n(K): c(K) ≤ [(g(K)+9)/6] and c(K) ≤ [(n(K) + 16)/12]. The (6n-2,3) torus knots show that these bounds are sharp.

Related

• Crosscap numbers of torus knots
• Linear Bounds of the Crosscap Number of Knots
• Average crosscap number of a 2-bridge knot
• Comparing nonorientable three genus and nonorientable four genus of torus knots
• Crosscap numbers of 2-bridge knots