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Knot Theory

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This is an overview of my work on knot theory, as well as resources I find useful. Some of these links are to websites which are occasionally down. Remember that they all are backed up by the wayback machine!

Dowker-Thistlethwaite to Planar-Diagram Notation Conversion

In order to find the upper bound for the bridge index of knots of a given crossing number, they must already be in PD notation. This has limited the knots computed to those with a crossing number at or below fourteen.

A long term project of mine has been to make a program to convert DT notation into PD notation. Since the DT representation of knots beyond fourteen crossings is readily available, this would allow the bridge indexes upper bound to be computed for higher crossing knots.

Resources

  1. The Knot Book -- Colin Adams -- ISBN-10: 0821836781
  2. The Knot Atlas
  3. Knot Info (Indiana University)

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