Nonnegative pinching, moduli spaces and bundles with infinitely many souls

Details Nonnegative pinching, moduli spaces and bundles with infinitely many souls Nonnegative pinching, moduli spaces and bundles with infinitely many souls

2004-11-08

arxiv.org/abs/math/0411179v2

Mathematics

Differential Geometry

Scientific paper

We show that in each dimension $n\ge 10$ there exist infinite sequences of homotopy equivalent but mutually non-homeomorphic closed simply connected Riemannian $n$-manifolds with $0\le \sec\le 1$, positive Ricci curvature and uniformly bounded diameter. We also construct open manifolds of fixed diffeomorphism type which admit infinitely many complete nonnegatively pinched metrics with souls of bounded diameter such that the souls are mutually non-homeomorphic. Finally, we construct examples of noncompact manifolds whose moduli spaces of complete metrics with $\sec\ge 0$ have infinitely many connected components.

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