Genuine laminations of 3-manifolds

DMS-0073029 William KazezKazez提出研究3-流形的真正层积。 他和他的同事D。Gabai，有兴趣了解几何形状的普遍覆盖的流形包含一个真正的层，特别是它是如何与几何形状的叶子的层。 他还建议研究表示的顺序树。 Kazez沿着与K.本田和G. Matic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单值性的双曲结，缝合流形分解非常简单，他们建议在这种情况下研究分类问题。Kazez，沿着他的合作者，建议研究叶理和接触结构之间的相互作用和关系。 这两种结构都是对三维空间中两个平面的家族的研究，但这些家族似乎非常不同。 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，随着周围空间沿着沿着表面分裂，深层关系开始变得明显。 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.