Mathematical Sciences: Automorphisms of the Free Group and Their Application to the Dynamics of Surface Diffeomorphisms

数学科学：自由群的自同构及其在表面微分同胚动力学中的应用

• 批准号: 8904934
• 负责人: Michael Handel
• 金额: $ 9.09万
• 依托单位: Research Foundation Of The City University Of New York (Lehman)
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-07-01 至 1992-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8904934&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Automorphisms; Free; Group

8904934 Handel The principal investigator will work on a pair of related projects, one concerning automorphisms of the free group and the other concerning the dynamics of surface diffeomorphisms. The first is a continuation of joint work with Mladen Bestvina. They hope to show that the group of outer automorphisms of the free group of rank n satisfies the Tits Alternative. They also hope to complete the characterization of geometric automorphisms that was begun earlier. The second project involves the computer implementation of algorithms developed earlier to determine the Thurston canonical form for an element of the mapping class group of a compact surface. Particular emphasis will be placed on the genus zero case, the goal being to understand the dynamics of a diffeomeophism f of the two-sphere by studying the canonical forms associated to f outside a finite invariant set.

8904934 HANDEL HANDEL将主要研究人员从事一对相关项目，一个关于自由组的自动形态，另一个涉及表面差异性的动态。 首先是与Mladen Bestvina进行联合合作的延续。 他们希望表明，自由等级N的外部自动形态群体满足山雀的替代方案。 他们还希望完成早些时候开始的几何自动形态的特征。 第二个项目涉及较早开发的算法的计算机实现，以确定紧凑型表面的映射类组的元素的瑟斯顿规范形式。 将特别重点放在零属的情况下，目的是通过研究在有限的不变式集合之外与f相关的规范形式来了解两杆的diffemoophism f的动力学。