Bounds on the Crosscap Number of Torus Knots
Thomas W. Mattman, Owen Sizemore
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.
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