Thesis advisor: Joshua E. Greene / We develop and implement obstructions to realizing a 3-manifold all of whose prime summands are lens spaces as Dehn surgery on a knot K in the Poincaré homology sphere, and in the process, we determine the knot Floer homology groups of a knot with such a surgery. We show that such a surgery never results in a 3-manifold with more than three non-trivial summands, and that if the result of surgery has exactly three non-trivial summands, then K is isotopic to a regular Seifert fiber. We furthermore identify the only two knots with half-integer lens space surgeries, and thus complete the classification of knots in the Poincaré homology sphere with non-integer lens space surgeries. We lastly show that a lens space L(p, q) that is realized as integer surgery on a knot K is realized as integer surgery on a Tange knot when p ≥ 2g(K). In order to do so, we build on Greene’s work on changemaker lattices and develop the theory of E8-changemaker lattices. / Thesis (PhD) — Boston College, 2023. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Mathematics.
| Identifer | oai:union.ndltd.org:BOSTON/oai:dlib.bc.edu:bc-ir_109706 |
| Date | January 2023 |
| Creators | Caudell, Jacob |
| Publisher | Boston College |
| Source Sets | Boston College |
| Language | English |
| Detected Language | English |
| Type | Text, thesis |
| Format | electronic, application/pdf |
| Rights | Copyright is held by the author. This work is licensed under a Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0). |
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