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BOUNDS ON THE CROSSCAP NUMBER OF TORUS KNOTS

THOMAS W. MATTMAN

Department of Mathematics and Statistics, California State University, Chico, Chico, CA 95929-0525, USA

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and

OWEN SIZEMORE

UCLA Mathematics Department, Box 951555, Los Angeles, CA 90095-1555, USA

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https://doi.org/10.1142/S0218216507005646Cited by:2 (Source: Crossref)

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.

Keywords:

AMSC: 57M25

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