Let ΓM be the fundamental group of a knot or link complement M. The discrete faithful representation of ΓM into PSL2(C) has an associated quaternion algebra. We can extend this notation to other representations, which are encoded by the character variety X(ΓM). The generalization is the canonical quaternion algebra and can be used to find unifying features of irreducible representations, such as the splitting behavior of their associated quaternion algebras. Within this dissertation, we will determine properties of the canonical quaternion algebra for the Whitehead link complement and explore how the algebra can descend to quaternion algebras of the Dehn (d, m)-surgeries thereon. / Mathematics
| Identifer | oai:union.ndltd.org:TEMPLE/oai:scholarshare.temple.edu:20.500.12613/8470 |
| Date | January 2023 |
| Creators | Palmer, Rebekah, 0000-0002-1240-6759 |
| Contributors | Stover, Matthew, Futer, David, Taylor, Samuel J., Chinburg, Ted, 1954- |
| Publisher | Temple University. Libraries |
| Source Sets | Temple University |
| Language | English |
| Detected Language | English |
| Type | Thesis/Dissertation, Text |
| Rights | IN COPYRIGHT- This Rights Statement can be used for an Item that is in copyright. Using this statement implies that the organization making this Item available has determined that the Item is in copyright and either is the rights-holder, has obtained permission from the rights-holder(s) to make their Work(s) available, or makes the Item available under an exception or limitation to copyright (including Fair Use) that entitles it to make the Item available., http://rightsstatements.org/vocab/InC/1.0/ |
| Relation | http://dx.doi.org/10.34944/dspace/8434, Theses and Dissertations |
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