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

数学科学：三维拓扑及相关代数中的一些问题

• 批准号: 9626537
• 负责人: G. Peter Scott
• 金额: $ 11.79万
• 依托单位: Regents of the University of Michigan - Ann Arbor
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-08-01 至 2000-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9626537&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Some; Problems; Dimensional

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. ***

9626537 Scott Scott 计划继续撰写有关 3 流形理论的书。 他还打算进一步探讨最近与澳大利亚墨尔本大学的 G. A. Swarup 联合完成的一些工作。 他们从三流形理论中发现了环空定理的代数版本，并且他们计划追求几个不同的研究方向。 他们的想法涉及斯科特早期一些工作的新应用，并且与 3-流形理论和几何群论中的重要工作密切相关。 这些想法应该可以简化其他作者最近的一些困难工作，并证明现有技术无法证明的新结果。 该项目的主题是某些类型的几何与群论之间的密切联系。 它汇集了这些不同领域的几位作者的想法，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联系的并且具有更普遍的适用性。 ***