Taut foliations, positive 3‐braids, and the L‐space conjecture

DOI10.1112/TOPO.12147zbMATH Open1457.57020arXiv1809.03959OpenAlexW3098827734WikidataQ122979034 ScholiaQ122979034MaRDI QIDQ5108905

Siddhi Krishna

Publication date: 6 May 2020

Published in: Journal of Topology (Search for Journal in Brave)

Abstract: 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. Additionally, we construct taut foliations in every closed 3-manifold obtained by $r$-framed Dehn surgery along a positive 1-bridge braid in $S^3$, where $r<g(K)$.

Full work available at URL: https://arxiv.org/abs/1809.03959

zbMATH Keywords

taut foliations\(L\)-space conjecturepositive \(3\)-braids

Mathematics Subject Classification ID

General geometric structures on low-dimensional manifolds (57M50) Knot theory (57K10) Homology theories in knot theory (Khovanov, Heegaard-Floer, etc.) (57K18) General topology of 3-manifolds (57K30)

Related Items (4)

Pretzel knots with \(L\)-space surgeries ⋮ Left-orderablity for surgeries on \((-2,3,2s + 1)\)-pretzel knots ⋮ L-spaces, taut foliations and the Whitehead link ⋮ Existence of Taut Foliations on Seifert Fibered Homology 3-spheres

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