Free Groups and Coherence

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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. ***