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The homotopy type of a Poincaré Duality Complex after looping

The homotopy type of a Poincaré Duality Complex after looping
The homotopy type of a Poincaré 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?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;Q)=0 and H n?1 (X;Z 2 )=0 . Then its loop space homotopy type is uniquely determined by the action of higher Bockstein operations on H n?1 (X;Z p ) for each odd prime p . A stronger result is obtained when localized at odd primes.
1-26
Beben, Piotr
a74d3e1f-52e0-4dc6-8f20-9c1628a20d2b
Wu, Jie
541b9f29-928c-4fbd-9697-2f567d76feb6
Beben, Piotr
a74d3e1f-52e0-4dc6-8f20-9c1628a20d2b
Wu, Jie
541b9f29-928c-4fbd-9697-2f567d76feb6

Beben, Piotr and Wu, Jie (2011) The homotopy type of a Poincaré Duality Complex after looping. Proceedings of the Edinburgh Mathematical Society, 1-26.

Record type: Article

Abstract

We 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 X be a (n?2) -connected finite orientable Poincar\'e (2n?1) -complex such that H n?1 (X;Q)=0 and H n?1 (X;Z 2 )=0 . Then its loop space homotopy type is uniquely determined by the action of higher Bockstein operations on H n?1 (X;Z p ) for each odd prime p . A stronger result is obtained when localized at odd primes.

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More information

Accepted/In Press date: 2011
Organisations: Mathematical Sciences

Identifiers

Local EPrints ID: 365618
URI: https://eprints.soton.ac.uk/id/eprint/365618
PURE UUID: 4dfdf864-fbc7-4f44-ac50-3e7184f07556

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Date deposited: 10 Jun 2014 15:15
Last modified: 18 Jul 2017 02:19

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