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- W3049693238 abstract "In his seminal 1976 paper Bill Thurston observed that a closed leaf S of a foliation has Euler characteristic equal, up to sign, to the Euler class of the foliation evaluated on [S], the homology class represented by S. The main result of this paper is a converse for taut foliations: if the Euler class of a taut foliation $mathcal{F}$ evaluated on [S] equals up to sign the Euler characteristic of S and the underlying manifold is hyperbolic, then there exists another taut foliation $mathcal{F'}$ such that $S$ is homologous to a union of leaves and such that the plane field of $mathcal{F'}$ is homotopic to that of $mathcal{F}$. In particular, $mathcal{F}$ and $mathcal{F'}$ have the same Euler class. In the same paper Thurston proved that taut foliations on closed hyperbolic 3-manifolds have Euler class of norm at most one, and conjectured that, conversely, any integral cohomology class with norm equal to one is the Euler class of a taut foliation. This is the second of two papers that together give a negative answer to Thurston's conjecture. In the first paper, counterexamples were constructed assuming the main result of this paper." @default.
- W3049693238 created "2020-08-21" @default.
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- W3049693238 date "2020-08-17" @default.
- W3049693238 modified "2023-09-22" @default.
- W3049693238 title "The fully marked surface theorem" @default.
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