Mathematical Sciences: Problems in Low Dimensional Manifolds

Long计划研究低维流形、辫子群和表示簇理论中几个相互关联的问题。具体目的是关于纽结流形上的外科手术及其基本群的剩余性质。这与映射类和辫子群有相互作用，其中要使用的技术包括映射类群的瑟斯顿理论。低维几何对象(流形)是3维空间居民研究的自然主题。

Long plans to examine several interrelated questions in the theory of low dimensional manifolds, braid groups and representation varieties. The specific aims concern surgeries on knot manifolds and residual properties of their fundamental groups. This has interactions with mapping class and braid groups, where the techniques to be used include the Thurston theory of mapping class groups. Low dimensional geometric objects (manifolds) are a natural subject for investigation by inhabitants of a 3-dimensional space.