Abstract
AbstractWe answer a weaker version of the classification problem for the homotopy types of (n — 2)-connected closed orientable (2n — 1)-manifolds. Let n ≥ 6 be an even integer and let X be an (n — 2)-connected finite orientable Poincaré (2n — 1)-complex such that Hn-1 (X;ℚ) = 0 and Hn-1 (X;ℤ2) = 0. Then its loop space homotopy type is uniquely determined by the action of higher Bockstein operations on Hn-1 (X; ℤp) for each odd prime p. A stronger result is obtained when localized at odd primes.
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