Publicacions Matemàtiques

Localization genus

Jesper M. Møller and Jérôme Scherer

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Which spaces look like an $n$-sphere through the eyes of the $n$-th Postnikov section functor and the $n$-connected cover functor? The answer is what we call the Postnikov genus of the $n$-sphere. We define in fact the notion of localization genus for any homotopical localization functor in the sense of Bousfield and Dror Farjoun. This includes exotic genus notions related for example to Neisendorfer localization, or the classical Mislin genus, which corresponds to rationalization.

Article information

Publ. Mat., Volume 61, Number 1 (2017), 259-281.

Received: 6 July 2015
Revised: 4 July 2016
First available in Project Euclid: 22 December 2016

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 55S45: Postnikov systems, $k$-invariants
Secondary: 55R15: Classification 55R70: Fibrewise topology 55P20: Eilenberg-Mac Lane spaces 22F50: Groups as automorphisms of other structures

Genus localization Postnikov section connected cover completion rationalization self equivalence


Møller, Jesper M.; Scherer, Jérôme. Localization genus. Publ. Mat. 61 (2017), no. 1, 259--281. doi:10.5565/PUBLMAT_61117_10.

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