A graph theoretic proof that Wada's type seven link invariant is determined by the double branched cover : a thesis presented in partial fulfilment of the requirements for the degree of Master of Science in Mathematics at Massey University, Manawatū, New Zealand
| dc.contributor.author | Solomon, Zachary Tancred | |
| dc.date.accessioned | 2022-07-12T20:26:35Z | |
| dc.date.available | 2022-07-12T20:26:35Z | |
| dc.date.issued | 2021 | |
| dc.description.abstract | The fundamental group of a link L is a group-valued link invariant that can be defined by assigning a generator to each arc of a link diagram of L, and introducing a relation between them at each crossing. Wada studied what he called shift representations to look for other crossing relations that might define group-valued link invariants. He found seven shift representations, two of which he noted do not define group-valued link invariants. One of the seven defines an infinite family Gm of invariants that includes the fundamental group as G₁, and these have since been shown to distinguish knots up to reflection for m ≥ 2. Wada showed that three of the remaining four give no new information, leaving just his type seven invariant, which we call W₇. Sakuma showed that the seventh of Wada’s shift representations is isomorphic to the free product of Z and the fundamental group of the double branched cover of L, π₁(L˜₂), that is W₇(L) ∼= π₁(L˜₂) ∗ Z. We will use graph theoretic methods to give a new proof of Sakuma’s result. | en |
| dc.identifier.uri | http://hdl.handle.net/10179/17333 | |
| dc.language.iso | en | en |
| dc.publisher | Massey University | en |
| dc.rights | The Author | en |
| dc.subject.anzsrc | 490401 Algebra and number theory | en |
| dc.title | A graph theoretic proof that Wada's type seven link invariant is determined by the double branched cover : a thesis presented in partial fulfilment of the requirements for the degree of Master of Science in Mathematics at Massey University, Manawatū, New Zealand | en |
| dc.type | Thesis | en |
| massey.contributor.author | Solomon, Zachary Tancred | |
| thesis.degree.discipline | Mathematics | en |
| thesis.degree.level | Masters | en |
| thesis.degree.name | Master of Science (MSc) | en |