The Homotopy Type of a Poincaré Duality Complex after Looping

Details The Homotopy Type of a Poincaré Duality Complex after Looping The Homotopy Type of a Poincaré Duality Complex after Looping

2011-02-08

arxiv.org/abs/1102.1516v10

Mathematics

Algebraic Topology

Fixed the statement of Theorem 3.5, and added Lemma 3.4 to clarify the proof. Fixed the proof of Lemma 6.3, though the stateme

Scientific paper

We give an answer to a weaker version of the classification problem for the homotopy types of $(n-2)$-connected closed orientable $(2n-1)$-manifolds. Let $n\geq 6$ be an even integer, and $X$ be a $(n-2)$-connected finite orientable Poincar\'e $(2n-1)$-complex such that $H^{n-1}(X;\mathbb{Q})=0$ and $H^{n-1}(X;\zmodtwo)=0$. Then its loop space homotopy type is uniquely determined by the action of higher Bockstein operations on $H^{n-1}(X;\zmodp)$ for each odd prime $p$. A stronger result is obtained when localized at odd primes.

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