Mathematical Sciences: Algebraic and Geometric Topology

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M. Davis and R. Charney intend to work on topics in geometric topology and geometric methods in group theory. They will apply Gromov's theory of non-positively curved spaces to Artin groups associated to infinite reflection groups. In addition, R. Charney will study building-like complexes and mapping class groups of surfaces with group actions, M. Davis will work on some problems concerning right-angled Coxeter orbifolds. All these projects involve very concrete geometry and some deceptively simple questions about an algebraic structure called a group. Traditionally, various groups have been used in the analysis of topological spaces. In these projects, however, topology can be expected to pay its dues to algebra by helping to answer some questions in group theory.