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The Quarterly Journal of Mathematics 2001 52(1):25-32; doi:10.1093/qjmath/52.1.25
© 2001 by Oxford University Press
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On compressing discs of torus knots

Michael T. Greene1 and Bert Wiest1

1 Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK, e-mail: mtg{at}uk.radan.com e-mail: bertw{at}pims.math.ca

We prove that every compressing disc of a (2n+1,2) -torus knot has at least 2n negative intersections with the knot; this implies that, in the language of [2], the natural framing is –2n. The proof uses an explicit and elementary simplification procedure for compressing discs.

Received 18 January 1999. Revised 11 October 1999.


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