This is a fascinating story, in any case. ]]>

Heegaard accepts geometric presentations on up to 26 generators and 32 relators. So for knots, Wirtinger presentations, or geometric presentations obtained using over-crossing and under-crossing arcs will work provided the 26 generator restriction is satisfied.

In practice, Heegaard determines each of the following examples is unknotted in only a few seconds.

Thistlethwaite’s Unknot from Wikipedia, Culprit from Kaufmann-Lambropoulou, Fig5 from Kaufmann-Lambropoulou, H) from Henrich & Kauffman, J) from Henrich & Kauffman, G) Goeritz’s unknot, Ochiai’s unknot 1 from “Non-trivial projections of the trivial knot” URL http://hdl.handlenet/2433/99940, Ochiai’s unknot 2 from the same paper, and Freedman’s Twisted Unknot.

Those wishing to check such things for themselves can obtain a current copy of Heegaard from me by email request to jberge at charter ‘dot’ net.

Note Heegaard is a Unix executable, which runs under terminal on an apple macintosh. So you will probably need a mac.

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