Publicacions Matemàtiques

Localization genus

Jesper M. Møller and Jérôme Scherer

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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.pm/1482375632

Digital Object Identifier
doi:10.5565/PUBLMAT_61117_10

Mathematical Reviews number (MathSciNet)
MR3590122

Zentralblatt MATH identifier
1370.55006

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

Keywords
Genus localization Postnikov section connected cover completion rationalization self equivalence

Citation

Møller, Jesper M.; Scherer, Jérôme. Localization genus. Publ. Mat. 61 (2017), no. 1, 259--281. doi:10.5565/PUBLMAT_61117_10. https://projecteuclid.org/euclid.pm/1482375632


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