Article contents
The Homotopy Type of a Poincaré Duality Complex After Looping
Published online by Cambridge University Press: 10 June 2015
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
- 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
References
- 10
- Cited by