Actions of discrete groups on nonpositively curved spaces
This note contains several observations concerning discrete groups of non-parabolic isometries of spaces of nonpositive curvature. We prove that (almost all) surface mapping class groups do not admit such actions; in particular, they do not act cocompactly. A new obstruction to the existence of a nonpositively curved metric on closed manifolds is presented. We give examples of 4-manifolds fibered over surfaces and of graph 3-manifolds fibered over the circle which do not admit metrics of nonpositive curvature.
scientific article; zbMATH DE number 952634