Free Groups and Coherence

9803289Feighn Mark Feighn与Mladen Bestvina和Michael Handel将继续研究自由群的自同构群。将描述阿贝尔子群。自由群的自同构群的曲面上的映射类群的Torelli子群是在第一同调上活动的子群。将Morse理论技术应用于Teichmuller空间或Culler-Vogtmann外空间的边界，以确定Torelli群的连通性。此外，还将进行对连贯群体的研究。群是基本的代数对象。它们描述了物体的对称性，因此在任何对称出现的地方都很重要。例如，分子的对称群在一定程度上决定了分子的化学性质。几何群论是一个新兴的、令人兴奋的数学领域，它从物体的几何性质中收集对称群的代数性质。当对象本身被视为一个组时，就会出现有趣的组。Mark feighn将继续将这种技术应用于研究一类有趣的群，即自由群的对称群。自由群体在群体理论中起着核心作用，因为任何群体都可以从自由群体中获得。＊＊＊

9803289Feighn Mark Feighn, with Mladen Bestvina and Michael Handel, will continuethe study of automorphism groups of free groups. Abelian subgroups willbe described. The Torelli subgroup of a mapping class group of a surfaceor of the automorphism group of a free group is the subgroup that actstrivially on first homology. Morse theoretic techniques will be appliedto bordifications of Teichmuller Space or Culler-Vogtmann's Outer Spacein order to determine connectedness properties of Torelli groups. Further,the study of coherent groups will be pursued. Groups are fundamental algebraic objects. They describe symmetries ofobjects and so are important anywhere symmetry appears. For example,the symmetry group of a molecule in part determines the molecule'schemical properties. In a new and exciting field of mathematics,geometric group theory, algebraic properties of the symmetry group of anobject are gleaned from geometric properties of the object. Interestinggroups occur when the object itself is taken to be a group. Mark Feighnwill continue to apply this technique in the study of a fascinatingclass of groups, the symmetry groups of free groups. Free groups play acentral role in the theory of groups, as any group may be obtained from afree group. ***