Taut foliations from double-diamond
                    replacements

Delman, Charles; Roberts, Rachel

doi:10.1090/conm/760/15288

Cited by 2 publications

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“…Taut foliations on surgeries on knots are constructed, for example, in [Rob01], [LR14], [DR19], [DR20], [Kri20] and it is possible to prove the left orderability of some of these manifolds by determining which of these foliations have vanishing Euler class, as done in [Hu19]. Another approach to study the left orderability of surgeries on knots is via representation theoretic methods, as presented in [CD18].…”

Section: Introductionmentioning

confidence: 99%

L-spaces, taut foliations and the Whitehead link

Santoro¹

2022

Preprint

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We prove that if M is a rational homology sphere that is a Dehn surgery on the Whitehead link, then M is not an L-space if and only if M supports a coorientable taut foliation. The left orderability of some of these manifolds is also proved, by determining which of the constructed taut foliations have vanishing Euler class.We also present some more general results about the structure of the L-space surgery slopes for links whose components are unknotted and with pairwise linking number zero, and about the existence of taut foliations on the fillings of a k-holed torus bundle over the circle with some prescribed monodromy. Our results, combined with some results from [RSS03], also imply that all the rational homology spheres that arise as integer surgeries on the Whitehead link satisfy the L-space conjecture. L-spacesIn this section we prove the first part of Theorem 1.1.We start by recalling some definitions and the main result of [RR17]. Let Y be a rational homology solid torus, i.e. Y is a compact oriented 3-manifold with toroidal boundary such that H * (Y ; Q) ∼ = H * (D 2 × S 1 ; Q).

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