Rational Homology 5-Spheres with Positive Ricci Curvature

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

2002-03-06

arxiv.org/abs/math/0203048v1

Mathematical Research Letters 9, 521-528 (2002)

Mathematics

Differential Geometry

8 pages

Scientific paper

We prove that for every integer 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 $\scriptstyle{k=p_1... p_r}$ for distinct primes $\scriptstyle{p_i}$ then $\scriptstyle{M^5_k}$ is uniquely determined.

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