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韩德尔首席研究员将致力于两个相关的项目，一个是关于自由群的自同构，另一个是关于表面微分同态的动力学。首先是继续与姆拉登·贝斯特维纳的联合工作。他们希望证明n阶自由群的外自同构群满足Tits择优。他们还希望完成早先开始的几何自同构的刻画。第二个项目涉及早先开发的算法的计算机实现，以确定紧致曲面的映射类群的元素的瑟斯顿标准形。重点将放在零亏格上，目的是通过研究与有限不变集外的f相关的典范形式来理解两个球面的微分同态态f的动力学。