Sutures, Taut Manifolds and the Topology of 3-Manifolds

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Hozoori, Surena | 2014

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 46064 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Esfahani Zadeh, Mostafa
Abstract:
In this essay we focus on the question of whether a 3-manifold (possibly with bound- ary) like M supports a codimension-1 transversely oriented foliation like F , such that F is transverse to ∂M and does not have Reeb components. If such foliation exists, then ∂M is necessarily a (possibly
empty) union of tori and (based on the works of Novikov, Reeb and Rosenberg) M is either S2 × S1(with F being the prod- uct foliation) or M is irreducible. In a paper by David Gabai, which we discuss, the suﬃciency of these conditions is proved in case of non-trivial second homology group.Furthermore, from the works of Thurston it is concluded that compact leaves of such foliation are norm minimizing and Gabai shows that conversely, every norm minimizing surface in such manifold can be realised as a compact leaf of such foliation
Keywords:
Foliation ; Sutured Manifold ; Three Dimentional Manifold ; Taut Foliations ; Knot Theory