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Thesis/Dissertation
Date
2023
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Mathematics
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http://dx.doi.org/10.34944/dspace/8434
Abstract
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.
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