Free Groups and Coherence

小行星9803289 马克Feighn，与Mladen Besthouts和迈克尔亨德尔，将继续研究自同构群的自由群体。 阿贝尔子群将被描述。 曲面的映射类群或自由群的自同构群的Torelli子群是对第一同调有作用的子群。 莫尔斯理论方法将被应用于Teichmuller空间或Culler-Vogtmann外层空间的边化，以确定Torelli群的连通性。 此外，还将继续对连贯群体进行研究。 群是基本的代数对象。 它们描述了物体的对称性，因此在任何出现对称性的地方都很重要。 例如，分子的对称群部分地决定了分子的化学性质。 在一个新的和令人兴奋的数学领域，几何群论，代数性质的对称群的一个对象收集的几何性质的对象。 当对象本身被视为一个组时，就会发生组。 马克费恩将继续适用于这种技术的研究一个fascinatingclass组，对称群的自由团体。 自由群在群论中起着中心作用，因为任何群都可以从自由群得到。***

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. ***