Essential Laminations

摘要：Roberts教授提出研究3流形中的基本层合。有两个主要的调查方向。首先，通过理解顺序树上的群体行为（与M. Stein教授合作），以及更直接地通过使用“标准形式”，更好地理解基本层的不存在性。第二种方法涉及搜索结构，这些结构可以提供关于结和连接的特殊手术的新信息。在这项研究中，罗伯茨教授调查了有关3-流形结构的问题，3-流形是由三维空间的块按照一定的规则拼凑而成的空间。总体而言，获得的空间通常非常复杂，并且模拟了许多有趣的现象。例如，我们的空间宇宙是一个三流形，理解这一点至关重要。三维流形的研究对研究三维空间中弦的打结和连接也很重要，而这对研究DNA的结构也很重要。

Proposal: DMS-9971333PI: Rachel RobertsAbstract: Professor Roberts proposes to study essential laminations in 3-manifolds. There aretwo main directions of investigation. The firstinvolves working at better understanding nonexistence of essential laminations, boththrough understanding group actions onorder trees (in collaboration with Professor M. Stein) and, moredirectly, throughthe use of``standard forms''. The secondinvolves searching for constructions which give new information about exceptionalsurgeries on knots and links.In this research, Professor Roberts investigatesquestions concerning the structure of 3-manifolds,which are spaces formed by piecingtogether blocks of 3-dimensional space accordingto certain rules. Globally, the spaces obtainedare usually quite complex and model manyinteresting phenomena. Our spatial universe,for example, is a 3-manifold which it is crucial to understand. The studyof 3-manifolds is also important in thestudy of the knotting and linking of stringsin 3-dimensional space, which in turn isimportant in the study of the structure of DNA.