Mathematical Sciences: Real Trees and Free Groups

数学科学：实树和自由群

• 批准号: 9302519
• 负责人: Mark Feighn
• 金额: $ 7.2万
• 依托单位: Rutgers University New Brunswick
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-07-01 至 1996-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9302519&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Real; Trees; Free

The mapping class group of a closed surface acts on compactified Teichmuller space. The topology of this space, as well as the dynamics of this action, are well understood and give information about global properties of the mapping class group. For example, it satisfies the Tits alternative. The project is to continue an analogous study of the outer automorphism group of the free group via its action on compactified outer space. Points in Outer Space are equivalence classes of simplicial metric trees. The compactifying points are classes of real trees, objects obtained from degenerations of simplicial trees. Groups abound in the physical sciences because they arise as the set of symmetries of an object. There is a special group, called the free group, from which all others may be constructed. The project is to continue the investigation of the basic structure of the free group. The technique is to use tools recently developed by E. Rips and generalized by the investigator with M. Bestvina.

封闭表面的映射类组作用于压实的Teichmuller空间。 该空间的拓扑以及该动作的动态已得到充分理解，并提供了有关映射类组的全球属性的信息。 例如，它可以满足山雀的选择。 该项目将通过其对压缩外层空间的作用继续对自由组的外部自动形态组进行类似研究。 外太空的点是简单公制树的等效类别。 压实点是真实树的类别，是从简单树的退化中获得的对象。 小组在物理科学中成熟，因为它们是对象的对称性集合。 有一个特殊的小组，称为自由小组，可以从中构建所有其他组。 该项目将继续调查自由组的基本结构。 该技术是使用E. RIPS最近开发的工具，并由M. bestvina的研究人员推广。