Essential Laminations

建议：DMS-9971333PI：Rachel Roberts摘要：Roberts教授建议研究三维流形中的基本分层。第一个涉及更好地理解本质层的不存在，既通过理解有序树上的群体行为(与M.Stein教授合作)，更直接地通过使用“标准形式”。在这项研究中，Roberts教授研究了关于三维流形的结构问题，三维流形是指按照一定的规则将三维空间的块拼凑在一起形成的空间。在全球范围内，所获得的空间通常是相当复杂的，并且模拟了许多有趣的现象。例如，我们的空间宇宙是一个3-流形，理解它是至关重要的。三维流形的研究对于研究三维空间中弦的打结和连接也很重要，而三维空间中弦的打结和连接又是研究DNA结构的重要方面。

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.