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Published online by Cambridge University Press: 22 January 2016
Let M be a complete simply-connected riemannian manifold of even dimension m. J. Dodziuk and I.M. Singer ([D1]) have conjectured that H2p(M) = 0 if p ≠ m/2 and dim H2m/2(M) = ∞, where H2*(M) is the space of L2-harmonic forms on M.