Berkenbosch, Fedel (2022) A one-cocycle evaluated on the rotation loop of a knot. Bachelor's Thesis, Mathematics.
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Abstract
Thomas Fiedler formulated a framework for constructing knot invariants based on one-cocyles evaluated on loops in the space of knots. We explain the necessary theory and clearly define and illustrate the definitions required for one of these cocycles, $R^{(2)}_{n,d^+}(a,r,K,\gamma)$, which was conjectured to be able to distinguish between mirrors. We give new direct but partial proofs of its invariance. It turns out that while the cocycle can not distinguish between mirrors its evaluation on the first half of the rotation loop gives rise to an equation that is able to distinguish between mirrors of knots, but is no longer an invariant.
| Item Type: | Thesis (Bachelor's Thesis) |
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| Supervisor name: | Veen, R.I. van der and Seri, M. |
| Degree programme: | Mathematics |
| Thesis type: | Bachelor's Thesis |
| Language: | English |
| Date Deposited: | 14 Jul 2022 11:42 |
| Last Modified: | 14 Jul 2022 11:47 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/27854 |
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