Mathematical Sciences: Some Problems in 3-Dimensional Topology and in Related Algebra

9626537斯科特·斯科特计划继续写他的关于3-流形理论的书。他还打算进一步探索最近与澳大利亚墨尔本大学的G.A.Swarup共同完成的一些工作。他们已经从3-流形理论中找到了环形定理的代数版本，并且他们计划追求几个不同的研究方向。他们的思想涉及Scott早期工作的新应用，并与3-流形理论和几何群论中的重要工作密切相关。这些想法应该会简化其他作者最近的一些困难工作，并证明用现有技术无法证明的新结果。这个项目的主题是某些类型的几何和群论之间的密切联系。它汇集了几位作者在这些不同领域的想法，这些想法最初似乎只适用于特殊情况，但现在被认为是相互关联的，具有更广泛的适用性。***

9626537 Scott Scott plans to continue work on his book on the theory of 3-manifolds. He also intends to explore further some recent work done jointly with G. A. Swarup of the University of Melbourne, Australia. They have found an algebraic version of the Annulus Theorem from the theory of 3-manifolds, and there are several different directions of inquiry that they plan to pursue. Their ideas involve new applications of some earlier work of Scott and are closely related to important work in the theory of 3-manifolds and in geometric group theory. These ideas should simplify some difficult recent work of other authors and prove new results that have been impossible to prove with the available techniques. The theme of this project is the close connection between certain types of geometry and group theory. It brings together ideas of several authors in these different areas that at first seemed to apply only in special situations but are now being seen to be connected and to have much more general applicability. ***