Rational Homology 5-Spheres with Positive Ricci Curvature

2002/03/06 by Charles P. Boyer, Krzysztof Galicki
Mathematics · #math.DG #math.AT #msc:53C25

paper · pdf

published as Mathematical Research Letters 9, 521-528 (2002) · 8 pages

arxiv created 2002/03/06 · arxiv updated 2009/11/30

Abstract

We prove that for every integer k>1 there is a simply connected rational homology 5-sphere \scriptstyleM⁵_k with spin such that \scriptstyleH₂(M⁵_k,\bbz) has order \scriptstylek², and \scriptstyleM⁵_k admits a Riemannian metric of positive Ricci curvature. Moreover, if the prime number decomposition of \scriptstylek has the form \scriptstylek=p₁... p_r for distinct primes \scriptstylep_i then \scriptstyleM⁵_k is uniquely determined.

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