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Platonic triangles of groups. (English) Zbl 0959.20039

Summary: Non-positively curved triangles of finite groups are of cohomological dimension 2 over the rationals and have Property FA. We classify triangles of finite groups which satisfy certain geometric conditions including the Gauss-Bonnet theorem. We investigate whether or not these groups are virtually torsion-free, contain a free Abelian subgroup of rank 2, are residually finite or are linear.

MSC:

20F67 Hyperbolic groups and nonpositively curved groups
20F65 Geometric group theory
20F55 Reflection and Coxeter groups (group-theoretic aspects)
20E06 Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations
53C23 Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces
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