Rational Homology 5-Spheres with Positive Ricci Curvature

We prove that for every integer $\scriptstyle{k >1}$ there is a simply connected rational homology 5-sphere $\scriptstyle{M^5_k}$ with spin such that $\scriptstyle{H_2(M^5_k,\bbz)}$ has order $\scriptstyle{k^2},$ and $\scriptstyle{M^5_k}$ admits a Riemannian metric of positive Ricci curvature. Moreover, if the prime number decomposition of $\scriptstyle{k}$ has the form $\scriptstyle{k=p_1\cdots p_r}$ for distinct primes $\scriptstyle{p_i}$ then $\scriptstyle{M^5_k}$ is uniquely determined.

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Published 1 January 2002