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Journal of the London Mathematical Society 2001 63(2):487-500; doi:10.1017/S0024610700001897
© 2001 by London Mathematical Society
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© The London Mathematical Society

Some Examples Related to 4-Genera, Unknotting Numbers and Knot Polynomials

A. Stoimenow

Max-Planck-Institut für Mathematik Vivatsgasse 7, D-53111 Bonn, Germany, alex{at}mpim-bonn.mpg.de

Received 20 December 1999. Revision received 13 March 2000.

The paper gives examples of knots with equal knot polynomials, but distinct signatures, 4-genera, double branched cover homology groups and unknotting numbers. This generalizes some examples given by Lickorish and Millett. It is also shown that there are knots with minimal (crossing number) diagrams of different unknotting number (thus answering a question of Bleiler), and an alternative proof is given of Rudolph's result that there are knots of ≤ 15n crossings with unit Alexander polynomial and 4-genus or unknotting number n.


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