L-spaces, taut foliations and the Whitehead link
arXiv:2201.01211 · doi:10.2140/agt.2024.24.3455
Abstract
We prove that if is a rational homology sphere that is a Dehn surgery on the Whitehead link, then is not an -space if and only if 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 -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 -holed torus bundle over the circle with some prescribed monodromy. Our results, combined with some results from Roberts--Shareshian--Stein, also imply that all the rational homology spheres that arise as integer surgeries on the Whitehead link satisfy the L-space conjecture.
Revised version. The statement of Lemma 2.6 has been corrected; the rest of the paper is unaffected. 51 pages, 37 figures. Accepted for publication in Algebraic and Geometric Topology
References in corpus (18)
- Holomorphic disks and genus bounds
- Knot Floer homology detects fibred knots
- Laminations and groups of homeomorphisms of the circle
- Floer Simple Manifolds and L-Space Intervals
- Laminar Branched Surfaces in 3-manifolds
- Approximating -foliations by contact structures
- Orderability and Dehn filling
- -space surgeries on links
- Approximations of foliations
- L-spaces, taut foliations, and graph manifolds
- L-space intervals for Graph Manifolds and Cables
- Links of plane curve singularities are L-space links
- Floer homology, group orderability, and taut foliations of hyperbolic 3-manifolds
- Persistently foliar composite knots
- Taut Foliations, Positive 3-Braids, and the L-Space Conjecture
- Taut foliations in knot complements
- Taut foliations in surface bundles with multiple boundary components
- L-space surgeries on satellites by algebraic links