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Igor Belegradek - Pinching and Pontrjagin classes

IGOR BELEGRADEK, Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario  L8S 4K1, Canada
Pinching and Pontrjagin classes

We proof some pinching theorems for the class ${\cal M}_{a,b,\pi, n}$of n-manifolds that have fundamental groups isomorphic to $\pi$ and that can be given complete Riemannian metrics of sectional curvatures within [a,b] where $a\le b<0$. For example, given a word-hyperbolic group $\pi$ and an integer n there exist $\epsilon=\epsilon(n,\pi)>0$such that the tangent bundle of any manifold in the class ${\cal
M}_{-1-\epsilon, -1, \pi, n}$ has has zero rational Pontrjagin classes.