This project has four components. The first component entails the study of higher dimensional filling invariants of groups, with emphasis on contructing examples exhibiting the full range of possible behavior. Forester and collaborators Brady, Bridson, and Shankar intend to develop general methods for computing such invariants, and to study the role of subgroup distortion and curvature. The second component concerns the construction of geometric structures for particular classes of groups, such as limit groups, and the study of the structure of subgroups and ends for these groups. In the third component Forester will investigate the classification of generalized Baumslag-Solitar groups and pursue applications. In the fourth component Forester will continue his work with Rourke on the multivariable adjunction problem, in the case of torsion-free groups. This work extends and devolops Klyachko's methods.
Group theory is the theory of symmetry, which plays a fundamental role in mathematics. Notions of symmetry (or "groups") arise very naturally in geometry, but also in other, more abstract, areas. In the field of geometric group theory one studies abstract groups by constructing geometric spaces, tailor-made for the groups at hand, in order to "see" the symmetry and understand it. This project involves the detailed study of the geometric spaces thus constructed.
