2004/12/13 by P. Svetlov, Svetlov, P. · 1 citation
Mathematics · #Advanced Operator Algebra Research #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #math.GT #msc:53C21
paper · pdf · doi:10.48550/arxiv.math/0412228
8 pages
arxiv created 2005/01/11 · arxiv updated 2009/12/01
An n-dimensional manifold M (n≥ 3) is called \it generalized graph manifold if it is glued of blocks that are trivial bundles of (n-2)-tori over compact surfaces (of negative Euler characteristic) with boundary. In this paper two obstructions for generalized graph manifold to be nonpositively curved are described. Each 3-dimensional generalized graph manifold with boundary carries a metric of nonpositive sectional curvature in which the boundary is flat and geodesic (B. Leeb). The last part of this paper contains an example of 4-dimensional generalized graph manifold with boundary, which does not admit a metric of nonpositive sectional curvature with flat and geodesic boundary.