Genuine laminations of 3-manifolds

DMS-0073029 William KazezKazez建议研究真正的3-流形分层。他和他的合作者D.Gabai感兴趣的是了解包含真正层压的流形的万能盖子的几何，特别是它如何与层压的叶子的几何关系。他还建议研究有序树的表示法。Kazez与K.Honda和G.马季奇试图从缝合流形分解的角度来理解紧接触结构的构造。对于具有伪Anosov单向型的纤维结，缝合流形的分解非常简单，他们建议在这种背景下研究分类问题。Kazez和他的合作者建议研究叶状和接触结构之间的相互作用和关系。这两个结构都是对三维空间中两个平面的家族的研究，但这两个家族似乎截然不同。一个是处处可积的，即与嵌入曲面相切，另一个是无处可积的。尽管如此，随着环境空间沿着表面被分割，深层次的关系开始变得明显。我们打算发展和利用的正是这些关系。

DMS-0073029William KazezKazez 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.