L–spaces, taut foliations and the Whitehead link

Santoro, Diego

doi:10.2140/agt.2024.24.3455

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L–spaces, taut foliations and the Whitehead link

Diego Santoro

Algebraic & Geometric Topology 24 (2024) 3455–3502

DOI: 10.2140/agt.2024.24.3455

Abstract

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 with two unknotted components and 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 of Roberts, Shareshian and Stein (2003), also imply that all the rational homology spheres that arise as integer surgeries on the Whitehead link satisfy the L–space conjecture.

Keywords

L–spaces, taut foliations, Whitehead link, orderability

Mathematical Subject Classification

Primary: 57K10, 57K18, 57K32, 57R30

References

Publication

Received: 1 February 2022

Revised: 19 September 2022

Accepted: 24 October 2022

Published: 7 October 2024

Authors

Diego Santoro
Scuola Normale Superiore Pisa Italy

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Volume 24, issue 6 (2024)