The Homotopy Type of a Poincar\'e Duality Complex after Looping
We answer 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...
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Main Authors | , |
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Format | Journal Article |
Language | English |
Published |
08.02.2011
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Subjects | |
Online Access | Get full text |
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Summary: | We answer 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
$H^{n-1}(X;\mathbb{Z}_2)=0$. Then its loop space homotopy type is uniquely
determined by the action of higher Bockstein operations on
$H^{n-1}(X;\mathbb{Z}_p)$ for each odd prime $p$. A stronger result is obtained
when localized at odd primes. |
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DOI: | 10.48550/arxiv.1102.1516 |