Koster, O.L. (2020) Vassiliev knot invariants and the Conway weight system. Bachelor's Thesis, Mathematics.
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Abstract
Vassiliev invariant are conjectured to form a complete knot invariant making them one of the most powerful types of knot invariants. First we will discuss the basic theory of knots and knot invariants, after which we will develop the theory of Vassiliev invariants. In order to study Vassiliev invariants effectively we will explain chord diagrams, weight systems and the Fundamental theorem of finite-type invariants. The fundamental theorem of finite-type invariants states that each Vassiliev invariant corresponds to a weight system, which means we can generate Vassiliev invariants from given weight system. In this thesis we will discuss a prove of this fundamental theorem. We will also solve the problem of the dimension of the vector space of Vassiliev invariants of a given order. In the end we define the Conway weight system, give its corresponding Vassiliev invariant and show a connection with the adjacency matrix of the intersection graph of the knot.
| Item Type: | Thesis (Bachelor's Thesis) |
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| Supervisor name: | Veen, R.I. van der |
| Degree programme: | Mathematics |
| Thesis type: | Bachelor's Thesis |
| Language: | English |
| Date Deposited: | 27 Jul 2020 08:36 |
| Last Modified: | 27 Jul 2020 08:36 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/22881 |
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