Genuine laminations of 3-manifolds

University Of Georgia Research Foundation Inc, Athens GA

Investigators

Abstract

DMS-0073029 William Kazez Kazez proposes to study genuine laminations of 3-manifolds. He and his collaborator, D. Gabai, are interested in understanding the geometry of the universal cover of a manifold containing a genuine lamination, and in particular how it is related to the geometry of the leaves of the lamination. He also proposes to study representations of order trees. Kazez along with K. Honda and G. Matic seek to understand the construction of tight contact structures from the point of view of a sutured manifold decomposition. For fibred knots with pseudo-Anosov monodromy, the sutured manifold decompositions are quite simple, and they propose to study the classification problem in this setting. Kazez, along with his collaborators, proposes to study the interaction and relationships between foliations and contact structures. Both structures are a study of a family of two planes in a 3-dimensional space, but these families appear to be extremely different. One is everywhere integrable, that is tangent to an embedded surface, the other is nowhere integrable. In spite of this, as the ambient space is split along surfaces, deep relationships start to become apparent. It is these relationships that we intend to develop and exploit.