#### Volume 21, issue 5 (2021)

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Taut foliations leafwise branch cover $S^2$

### Danny Calegari

Algebraic & Geometric Topology 21 (2021) 2523–2541
##### Abstract

A cooriented foliation $\mathsc{ℱ}$ of an oriented $3$–manifold $M$ is taut if and only if there is a map from $M$ to the $2$–sphere whose restriction to every leaf is a branched cover.

##### Keywords
taut foliation, Riemann surface lamination, branched cover, leafwise holomorphic function
##### Mathematical Subject Classification
Primary: 57M50, 57R30
##### Publication
Received: 5 April 2020
Revised: 29 August 2020
Accepted: 22 September 2020
Published: 31 October 2021
##### Authors
 Danny Calegari Department of Mathematics University of Chicago Chicago, IL United States