Perturbed Traceless SU(2) Character Varieties of Tangle Sums
One strategy to study a link L is to decompose it into two tangles, T1 and T2, along a sphere intersecting the link in four points. Then information about the about the link L can be gleaned by studying the intersections of the (possibly perturbed) traceless SU(2) character varieties of T1 and T2 in...
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| Format: | Dissertation |
| Language: | English |
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ProQuest Dissertations & Theses
01-01-2023
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| Online Access: | Get full text |
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| Summary: | One strategy to study a link L is to decompose it into two tangles, T1 and T2, along a sphere intersecting the link in four points. Then information about the about the link L can be gleaned by studying the intersections of the (possibly perturbed) traceless SU(2) character varieties of T1 and T2 in a space called the pillowcase. In this thesis, the central question addressed is to identify the (perturbed) character variety of the sum of two tangles, as defined by Conway. The primary application of the result is showing that a map from tangles to bounding cochains of their perturbed character varieties conjectured to exist by Cazassus, Herald, Kirk, and Kotelskiy must be nontrivial. Other applications include showing that the Chern-Simons invariants for prime Montesinos links are rational and classifying all SU(2)-simple Montesinos links. |
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| ISBN: | 9798379705756 |