L-spaces, taut foliations and fibred hyperbolic two-bridge links

Santoro, Diego

doi:10.2140/agt.2026.26.1115

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

Submission form

Editorial board

Subscriptions

ISSN (electronic): 1472-2739

ISSN (print): 1472-2747

Author index

To appear

Other MSP journals

$L$-spaces, taut foliations and fibred hyperbolic two-bridge links

Diego Santoro

Algebraic & Geometric Topology 26 (2026) 1115–1154

DOI: 10.2140/agt.2026.26.1115

Abstract

We prove that if $M$ is a rational homology sphere that is Dehn surgery on a fibred hyperbolic two-bridge link, then $M$ is not an $L$ -space if and only if $M$ supports a co-orientable taut foliation. As a corollary we show that if $K^{'}$ is obtained by a nontrivial knot $K$ as a result of an operation called two-bridge replacement, then all nonmeridional surgeries on $K^{'}$ support co-orientable taut foliations. This operation generalises Whitehead doubling and as a particular case we deduce that all nonmeridional surgeries on Whitehead doubles of a nontrivial knot support co-orientable taut foliations.

Keywords

$L$-spaces, taut foliations, $L$-space conjecture, Dehn surgery, two-bridge links

Mathematical Subject Classification

Primary: 57M50

Secondary: 57K10

References

Publication

Received: 14 September 2024

Revised: 4 March 2025

Accepted: 16 April 2025

Published: 1 April 2026

Authors

Diego Santoro
University of Vienna Vienna Austria

Open Access made possible by participating institutions via Subscribe to Open.

Volume 26, issue 3 (2026)