Sutures, Taut Manifolds and the Topology of 3-Manifolds, M.Sc. Thesis Sharif University of Technology ; Esfahani Zadeh, Mostafa (Supervisor)
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... Cataloging briefSutures, Taut Manifolds and the Topology of 3-Manifolds, M.Sc. Thesis Sharif University of Technology ; Esfahani Zadeh, Mostafa (Supervisor)
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... Find in contentBookmark |
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