3-Manifolds and Geometric Group Theory

3-流形和几何群论

• 批准号: 9971555
• 负责人: G. Peter Scott
• 金额: $ 8.59万
• 依托单位: Regents of the University of Michigan - Ann Arbor
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1999
• 资助国家: 美国
• 起止时间: 1999-08-01 至 2002-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9971555&HistoricalAwards=false
• 关键词: Manifolds; Geometric; Group; Theory

Proposal: DMS-9971555PI: Peter ScottAbstract: The proposer plans to investigate purely algebraic analogs of the theoryof the characteristic submanifold of a Haken 3-manifold. Some results inthis direction have already been obtained by several authors but theiruniqueness results are much weaker than that in the 3-manifold context. Itis expected that such results should also yield new understanding of thepurely topological theory of 3-manifolds. The universe appears to be 3-dimensional and it is a very interestingquestion to understand its shape. There is an abstract theory of spacescalled 3-manifolds which attempts to describe all the possibilities forthe shape of such a space. While this theory is not complete, there is agreat deal known. In particular, many (and perhaps all) such spaces can bedecomposed into simple geometric pieces in a natural way. In thisproposal, it is planned to investigate further the properties of thisdecomposition into geometric pieces.

提案：DMS-9971555 PI：Peter Scott摘要：提出者计划研究Haken 3-流形的特征子流形理论的纯代数类似物。这方面的一些结果已经被一些作者得到，但他们的唯一性结果比在三维流形上的结果弱得多。期望这些结果也能对三维流形的纯拓扑理论产生新的认识。 宇宙看起来是三维的，理解它的形状是一个非常有趣的问题。有一种抽象的空间理论叫做三维流形，它试图描述这种空间形状的所有可能性。虽然这个理论还不完整，但有一个很大的交易。特别是，许多（也许是所有）这样的空间可以被分解成简单的几何件在一个自然的方式。在这个建议中，计划进一步研究这种分解成几何块的性质。