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Please use this identifier to cite or link to this item: http://arks.princeton.edu/ark:/88435/dsp01zg64tp54v
 Title: On Thurston's Euler class one conjecture Authors: Yazdi, Mehdi Advisors: Gabai, David Contributors: Mathematics Department Keywords: 3-manifoldsEuler classlow dimensional Topologytaut foliationThurston norm Subjects: Mathematics Issue Date: 2017 Publisher: Princeton, NJ : Princeton University Abstract: In 1976, Thurston proved that taut foliations on closed hyperbolic 3-manifolds have Euler class of norm at most one, and conjectured that, conversely, any Euler class with norm equal to one is Euler class of a taut foliation. We construct the first counterexamples to this conjecture, infinitely many indeed. The counterexamples are constructed by Dehn surgeries on certain fibered hyperbolic 3-manifolds. Moreover, they are constructive in the sense that the monodromy of the fibration map is given in terms of Dehn twists and the surgery coefficient is specified. We also suggest an alternative conjecture in terms of faithful representations of the fundamental group of the 3-manifold into certain group of homeomorphisms. URI: http://arks.princeton.edu/ark:/88435/dsp01zg64tp54v Alternate format: The Mudd Manuscript Library retains one bound copy of each dissertation. Search for these copies in the library's main catalog: catalog.princeton.edu Type of Material: Academic dissertations (Ph.D.) Language: en Appears in Collections: Mathematics

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