On Thurston’s Euler class-one conjecture

In 1976, Thurston proved that taut foliations on closed hyperbolic $3$-manifolds have Euler class of norm at most $1$, and conjectured that conversely, any integral second cohomology class with norm equal to one is the Euler class of a taut foliation. This is the first from a series of two papers that together give a negative answer to Thurston’s conjecture. Here counter-examples have been constructed conditional on the fully marked surface theorem. In the second paper, joint with David Gabai, a proof of the fully marked surface theorem is given.

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Received 19 July 2018

Received revised 8 June 2020

Accepted 1 August 2020

Published 21 January 2021