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Pictures from Work Brief Abstract
Pictures from Work Brief Abstract
In joint work with Carolyn Engelhardt, we pair braid dynamics, results on bridge position, and distance in the curve complex to obtain a sequence of hyperbolic knots. We conjecture about the relationships between knot genus, topological entropy, and distance in the curve complex.
In joint work with Carolyn Engelhardt, we pair braid dynamics, results on bridge position, and distance in the curve complex to obtain a sequence of hyperbolic knots. We conjecture about the relationships between knot genus, topological entropy, and distance in the curve complex.
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Putting a knot diagram into bridge position allows geometric arguments to be made the knot and its exterior. On the other hand, putting a knot into plat position gives a lot of algebraic information. This paper shows that bridge isotopy and plat isotopy are equivalent. This allows a “translation” of results from each way of looking at a knot diagram.
Putting a knot diagram into bridge position allows geometric arguments to be made the knot and its exterior. On the other hand, putting a knot into plat position gives a lot of algebraic information. This paper shows that bridge isotopy and plat isotopy are equivalent. This allows a “translation” of results from each way of looking at a knot diagram.
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Select Link Below:
The link provided below is to a repository of code written by Greg Vinal and I to perform calculations required for our work on rectangular diagram and plat unknotting. The code is written in Python and Sage. Some functions of note:
The link provided below is to a repository of code written by Greg Vinal and I to perform calculations required for our work on rectangular diagram and plat unknotting. The code is written in Python and Sage. Some functions of note:
- An algorithm to generate arbitrarily difficult unknots, called the Nutty Knotter. (See braids on the left. All have unknotted plat closures. )
- An algorithm that takes the braid word corresponding to a plat closure and draws a special rectangular diagram corresponding to the braid word.
- An algorithm that takes the vertex and edge set of a rectangular diagram and provides a braid word whose standard braid closure is in the same link type as the rectangular diagram. It then uses SnapPy to compute Jones polynomial, Seifert Genus etc.
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