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On Thurston’s Euler class-one conjecture

Mehdi Yazdi Mathematical Institute, University of Oxford, United Kingdom

TBD mathscidoc:2203.43004

Acta Mathematica, 225, (2), 313-368, 2020.12
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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@inproceedings{mehdi2020on,
  title={On Thurston’s Euler class-one conjecture},
  author={Mehdi Yazdi},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220310105905096334919},
  booktitle={Acta Mathematica},
  volume={225},
  number={2},
  pages={313-368},
  year={2020},
}
Mehdi Yazdi. On Thurston’s Euler class-one conjecture. 2020. Vol. 225. In Acta Mathematica. pp.313-368. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220310105905096334919.
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