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# Mathematical Research Letters

## Volume 9 (2002)

### Number 4

### Rational Homology 5-Spheres with Positive Ricci Curvature

Pages: 521 – 528

DOI: http://dx.doi.org/10.4310/MRL.2002.v9.n4.a12

#### Authors

#### Abstract

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.