Bounds on the Crosscap Number of Torus Knots
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.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.