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The celebrated theorem of Preissmann says that if M is a compact manifold carrying a riemannian metric of strictly negative curvature then the fundamental group 7ri(M) of M has the property (P) that every non-trivial abelian subgroup is isomorphic to Z. Since M is also a lf(7ri(M), l)-manifold (cf. [Mi, p. 103]) it is determined up to homotopy by 7ri(M). More generally, it was proved in [FJ1, Corollary 10.5] that, in dimensions bigger than 4, 7ri(M) determines M up to homeomorphism type. Hence one would expect strong inter-relations between the algebraic structure of 7ri(M) and the geometry of M, when M is a closed K^i^M), l)-manifold, and a natural question (cf. [BK, (6.2.1)]) to ask would be the following: If TT^M) has property (P), does M necessarily admit a metric of negative curvature? While this question still remains open, we prove, in this paper, that there are a large class of closed manifolds M which are i^yr^M), l)-manifolds and such that 7ri(M) shares all the properties of the fundamental group of certain compact nonpositively curved manifolds whereas M does not admit any metric of nonpositive curvature. In fact, we construct two classes of examples of compact topological manifolds M supporting at least two distinct smooth structures Mi and M2 where Mi is a compact, rank 1 (in the sense of [BBE]) nonpositively curved manifold while M2 cannot support a nonpositively curved metric. These constructions are motivated by and closely follow the paper [FJ4] where exotic smoothings of complete, finite volume, real hyperbolic manifolds which do

Rank 1 aspherical manifolds which do not support any nonpositively curved metric