Rigidity and Other Topological Aspects of Compact Nonpositively Curved Manifolds

  title={Rigidity and Other Topological Aspects of Compact Nonpositively Curved Manifolds},
  author={Lloyd E. Jones},
Let M be a compact connected Riemannian manifold whose sectional curvature values are all nonpositive. Let T denote the fundamental group of M. We prove that any homotopy equivalence ƒ : N —> M from a compact closed manifold TV is homotopic to a homeomorphism, provided that m > 5 where m = dim M . We show that the surgery L-group Lk+m(T, w{) is isomorphic to the set of homotopy classes of k k maps [M x I rel d , GI TOP], where / is the Ac-dimensional cube (with k > 0 ). We also show that the… CONTINUE READING
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