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The Homotopy Type of a Poincaré Duality Complex After Looping

Published online by Cambridge University Press:  10 June 2015

Piotr Beben  and
Jie Wu
Piotr Beben
Affiliation:
School of Mathematics, University of Southampton, Southampton SO17 1BJ, UK (p.d.beben@soton.ac.uk)
Jie Wu
Affiliation:
Department of Mathematics, National University of Singapore, Block S17 (SOC1), 10 Lower Kent Ridge Road, Singapore 119076 (matwuj@nus.edu.sg)
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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 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.

Keywords

Poincaré duality complexloop spacehomotopy classification of manifoldsPrimary 55P3555P1557N65
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 58 , Issue 3 , October 2015 , pp. 581 - 616
Copyright
Copyright © Edinburgh Mathematical Society 2015 

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