Interchanging Two Notations for Double-torus Links
Knot theory is a relatively young branch of mathematics, still less than a century old. The development of the Jones polynomial in 1984 led to increased activity in knot theory. Though work is constantly being done in this field, notably the classification of torus knots, double-torus knots are still...
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| Format: | Others |
| Language: | English |
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Digital Commons @ East Tennessee State University
2016
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| Online Access: | https://dc.etsu.edu/etd/2616 https://dc.etsu.edu/cgi/viewcontent.cgi?article=4003&context=etd |
| Summary: | Knot theory is a relatively young branch of mathematics, still less than a century old. The development of the Jones polynomial in 1984 led to increased activity in knot theory. Though work is constantly being done in this field, notably the classification of torus knots, double-torus knots are still lacking such a complete understanding. There exists two notations, those of Rick Norwood and of Peter Hill, that describe knots on the double-torus. The ambition of this thesis is to begin to make the case that it is possible to render these two notations interchangeable. Illustrating this will require examining the two notations and finding a way to change one into the other, then check if this process is reversible. If not, then proceed to develop a method that works to convert the second notation back to the first. |
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