4-dimensional locally CAT(0)-manifolds with no Riemannian smoothings
4-dimensional locally CAT(0)-manifolds with no Riemannian smoothings
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DOI：
10.1215/00127094-1507259
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发表时间：
2010-02
影响因子：
2.5
通讯作者：
M. Davis;T. Januszkiewicz;J.-F. Lafont
中科院分区：
文献类型：
--
作者：
M. Davis;T. Januszkiewicz;J.-F. Lafont
We construct examples of 4-dimensional manifolds M supporting a locally CAT(0)metric, whose universal covers Q M satisfy Hruska’s isolated flats condition, and contain 2-dimensional flats F with the property that @1F S S ,! S S @1 Q M are nontrivial knots. As a consequence, we obtain that the group 1.M/ cannot be isomorphic to the fundamental group of any compact Riemannian manifold of nonpositive sectional curvature. In particular, if K is any compact locally CAT(0)-manifold, then M K is a locally CAT(0)-manifold which does not support any Riemannian metric of nonpositive sectional curvature.
