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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the homology of Postnikov fibres


Authors: Y. Félix and J. C. Thomas
Journal: Proc. Amer. Math. Soc. 118 (1993), 255-258
MSC: Primary 55S45; Secondary 55S35, 57T05
MathSciNet review: 1165053
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Abstract: Let $ k$ be a field of positive characteristic and $ X$ be a simply connected space of the homotopy type of a finite type CW complex. The Postnikov fibre $ {X_{[n]}}$ of $ X$ is defined as the homotopy fibre of the $ n$-equivalence $ {f_n}:X \to {X_n}$ coming from the Postnikov tower $ \{ {X_n}\} $ of $ X$. We prove that if the Lusternik-Schnirelmann category of $ X$ is finite, then $ {H_{\ast}}({X_{[n]}};k)$ contains a free module on a subalgebra $ K$ of $ {H_{\ast}}(\Omega {X_n};k)$ such that $ {H_{\ast}}(\Omega {X_n};k)$ is a finite-dimensional free $ K$-module.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1165053-0
PII: S 0002-9939(1993)1165053-0
Keywords: Eilenberg-Mac Lane spaces, Postnikov tower, grade of a module, Lusternik-Schnirelmann category of a space
Article copyright: © Copyright 1993 American Mathematical Society