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

8904934 亨德尔 首席研究员将研究一对相关的 项目，一个关于自由群的自同构， 另一个是关于表面非同构的动力学。 第一个是继续与姆拉登·贝斯特韦斯特的联合工作。 他们希望证明， 秩为n的自由群满足Tits Alternative。 他们还 希望能完成几何的表征 自同构是较早开始的。 第二个项目涉及计算机执行 早期开发的算法，以确定瑟斯顿 的映射类群的元素的标准形式 致密表面 将特别强调 属零的情况下，目标是了解动态的一个 通过研究正则球面， 在有限不变集之外与f相关联的形式。

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.