80 research outputs found
Pinching, Pontrjagin classes, and negatively curved vector bundles
We prove several finiteness results for the class of
-manifolds that have fundamental groups isomorphic to and that can be
given complete Riemannian metrics of sectional curvatures within where
. In particular, if is a closed negatively curved manifold of
dimension at least three, then only finitely many manifolds in the class
are total spaces of vector bundles over . Furthermore,
given a word-hyperbolic group and an integer there exists a positive
such that the tangent bundle of any manifold in the
class has zero rational Pontrjagin classes.Comment: 32 page
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