Mathematical Sciences: Combinatorial Group Theory

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This project will study groups through curvature conditions on simplicial complexes with these groups as their fundamental groups. A generalization of small cancellation theory is given and it is proposed to study these small cancellation groups and their finitely presented subgroups by curvature conditions. Higher dimensional analogues are proposed with applications to classes of groups traditionally studied by geometric methods. A group is an algebraic object having a binary operation defined on it. Such objects are of interest to many different branches of mathematics and physics. This project will study these groups by geometric methods.