Essential Laminations

提案：DMS-9971333 PI：Rachel Roberts摘要：Roberts教授提出研究3-流形中的基本叠层。有两个主要的研究方向。第一个涉及到更好地理解不存在的基本层压，boththrough理解组行动的顺序树（在合作教授M。Stein），更直接地说，通过使用“标准形式”。第二部分涉及寻找结构，这些结构提供了关于结和链接上的异常手术的新信息。在这项研究中，罗伯茨教授研究了关于3-流形的结构的问题，3-流形是根据一定的规则将3维空间的块拼接在一起形成的空间。在全球范围内，所获得的空间通常相当复杂，并模拟了许多有趣的现象。例如，我们的空间宇宙是一个三维流形，理解它是至关重要的。三维流形的研究在三维空间中弦的打结和连接的研究中也很重要，而这反过来又在DNA结构的研究中很重要。

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.