Homology, Homotopy and Applications

Volume 16 (2014)

Number 1

Postnikov towers with fibers generalized Eilenberg–Mac Lane spaces

Pages: 139 – 157

DOI: https://dx.doi.org/10.4310/HHA.2014.v16.n1.a8

Authors

Kouyemon Iriye (Department of Mathematics and Information Sciences, Osaka Prefecture University, Sakai, Japan)

Daisuke Kishimoto (Department of Mathematics, Kyoto University, Kyoto, Japan)

Abstract

A generalized Postnikov tower (GPT) is defined as a tower of principal fibrations with the classifying maps into generalized Eilenberg–Mac Lane spaces. We study fundamental properties of GPT’s such as their existence, localization and length. We further consider the distribution of torsion in a GPT of a finite complex, motivated by the result of McGibbon and Neisendorfer. We also give an algebraic description of the length of a GPT of a rational space.

Keywords

Postnikov tower, generalized Eilenberg–Mac Lane space, localization, Postnikov length

2010 Mathematics Subject Classification

55P60, 55S45

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Published 2 June 2014