Admiraal, Jamara (2025) Surface knots, ch-diagrams, and the knot group. Bachelor's Thesis, Mathematics.
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Abstract
This thesis investigates surface knots, that is, closed connected surfaces in fourspace. We begin by introducing the core notions for working with surface knots and reviewing several standard representations, with a particular focus on chdiagrams and ab-surfaces. These serve as a tool for visualizing and manipulating surface knots to help determine when two surface knots are equivalent. Building upon the well-established theory for classical knots, we discuss the Wirtinger presentation to determine the knot group, which is an important algebraic invariant given by the fundamental group of the knot complement. Using ch-diagrams, we derive an altered version of the Wirtinger presentation that describes the knot group of surface knots. Furthermore, we explore the construction of (twist-)spun knots, which are obtained by spinning classical knots in four-space, and compute their associated knot groups using the developed presentation method. The results obtained from the adapted Wirtinger presentation are cross-referenced with known results in the literature to verify their consistency and correctness.
| Item Type: | Thesis (Bachelor's Thesis) |
|---|---|
| Supervisor name: | Veen, R.I. van der and Martynchuk, N. |
| Degree programme: | Mathematics |
| Thesis type: | Bachelor's Thesis |
| Language: | English |
| Date Deposited: | 14 Nov 2025 12:44 |
| Last Modified: | 03 Mar 2026 12:00 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/37130 |
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