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.authorSolomon, Zachary Tancred
dc.date.accessioned2022-07-12T20:26:35Z
dc.date.available2022-07-12T20:26:35Z
dc.date.issued2021
dc.description.abstractThe 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.urihttp://hdl.handle.net/10179/17333
dc.language.isoenen
dc.publisherMassey Universityen
dc.rightsThe Authoren
dc.subject.anzsrc490401 Algebra and number theoryen
dc.titleA 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 Zealanden
dc.typeThesisen
massey.contributor.authorSolomon, Zachary Tancred
thesis.degree.disciplineMathematicsen
thesis.degree.levelMastersen
thesis.degree.nameMaster of Science (MSc)en
Files
Original bundle
Now showing 1 - 1 of 1
Loading...
Thumbnail Image
Name:
SolomonMScThesis.pdf
Size:
403.14 KB
Format:
Adobe Portable Document Format
Description:
License bundle
Now showing 1 - 1 of 1
Loading...
Thumbnail Image
Name:
license.txt
Size:
3.32 KB
Format:
Item-specific license agreed upon to submission
Description: