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Title: On Thurston's Euler class one conjecture
Authors: Yazdi, Mehdi
Advisors: Gabai, David
Contributors: Mathematics Department
Keywords: 3-manifolds
Euler class
low dimensional Topology
taut foliation
Thurston 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.
Alternate format: The Mudd Manuscript Library retains one bound copy of each dissertation. Search for these copies in the library's main catalog:
Type of Material: Academic dissertations (Ph.D.)
Language: en
Appears in Collections:Mathematics

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