Welcome to Knots, Rick Norwood's website about knot theory and double-torus knots.

(-1/1, -2/2, -1/1)

This page includes a perl program that allows you to enter the t/i numbers of a double-trorus knot and view the Alexander polynomial of that knot.

You can contact me by e-mail at norwoodr@etsu.edu.

Enter the t/i numbers below and you can view the Seifert matrix and Alexander polynomial of a double-torus knot.

If the t/i numbers represent a link rather than a knot, you will get the message, "DID NOT CLOSE PATH."

Entries must be integers; denominators must be non-negative; the sum of the denominators must be even, and the middle denominator must be at least as large as the other two denominators. This program does not yet allow the middle denominator to be greater than the sum of the other two.

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Here is a link to a program that generates the Seifert matrix and Alexander polynomial.

This next program should turn a knot inside-out given its t/i numbers.

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Here is a link to a program that turns the double-torus knot inside-out.
And here is a link to the command-line version.

This page is a work in progress.

References

[1] F. Norwood, Curves on Surfaces, Topology and its Applications 33 (1989) 241-246

[2] R. Norwood, Turning Double-Torus Links Inside Out, J. Knot Theory Ramifications 8 (1999) 789-798

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