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Taut foliations, positive braids, and the L-space conjecture:

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.

Identiferoai:union.ndltd.org:BOSTON/oai:dlib.bc.edu:bc-ir_108731
Date January 2020
CreatorsKrishna, Siddhi
PublisherBoston College
Source SetsBoston College
LanguageEnglish
Detected LanguageEnglish
TypeText, thesis
Formatelectronic, application/pdf
RightsCopyright is held by the author, with all rights reserved, unless otherwise noted.

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