Silvans, Albert (2020) Observations on Almost OU Tangles. Bachelor's Thesis, Mathematics.
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Abstract
In the paper ''Over then UnderTangles"of Dror Bar-Natan, Zsuzsanna Dancso, and Roland van der Veen (2020), the authors focused on a subset of tangles, in which each component had its crossing arranged in a particular order: first all over crossings, then all under crossings, those we call OU tangles, or Over then Under tangles. They set out to prove that for each tangle there is a unique OU presentation, hence a Canonical form. Their approach involved an algorithm to bring a tangle into OU form, however they discovered that not all tangles admit an OU form, instead all the tangles that can be put into an OU form are related to Braids. In this paper we explore the effects of the above mentioned algorithm applied to tangles that do not have an OU form, we find out that the structures produced are indeed complicated, and we produce a tangle diagram drawing algorithm along the way.
| Item Type: | Thesis (Bachelor's Thesis) |
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| Supervisor name: | Veen, R.I. van der and Sterk, A.E. |
| Degree programme: | Mathematics |
| Thesis type: | Bachelor's Thesis |
| Language: | English |
| Date Deposited: | 06 Nov 2020 10:57 |
| Last Modified: | 06 Nov 2020 10:57 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/23572 |
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