Thesis advisor: Joshua E. Greene / We construct taut foliations in every closed 3-manifold obtained by r-framed Dehn surgery along a positive 3-braid knot K in S^3, where r < 2g(K)-1 and g(K) denotes the Seifert genus of K. This confirms a prediction of the L--space conjecture. For instance, we produce taut foliations in every non-L-space obtained by surgery along the pretzel knot P(-2,3,7), and indeed along every pretzel knot P(-2,3,q), for q a positive odd integer. This is the first construction of taut foliations for every non-L-space obtained by surgery along an infinite family of hyperbolic L-space knots. We adapt our techniques to construct taut foliations in every closed 3-manifold obtained along r-framed Dehn surgery along a positive 1-bridge braid, and indeed, along any positive braid knot, in S^3, where r < g(K)-1. These are the only examples of theorems producing taut foliations in surgeries along hyperbolic knots where the interval of surgery slopes is in terms of g(K). / Thesis (PhD) — Boston College, 2020. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Mathematics.
| Identifer | oai:union.ndltd.org:BOSTON/oai:dlib.bc.edu:bc-ir_108731 |
| Date | January 2020 |
| Creators | Krishna, Siddhi |
| 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, with all rights reserved, unless otherwise noted. |
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