Open Access
2017 Localization genus
Jesper M. Møller, Jérôme Scherer
Publ. Mat. 61(1): 259-281 (2017). DOI: 10.5565/PUBLMAT_61117_10


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.


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Jesper M. Møller. Jérôme Scherer. "Localization genus." Publ. Mat. 61 (1) 259 - 281, 2017.


Received: 6 July 2015; Revised: 4 July 2016; Published: 2017
First available in Project Euclid: 22 December 2016

zbMATH: 1370.55006
MathSciNet: MR3590122
Digital Object Identifier: 10.5565/PUBLMAT_61117_10

Primary: 55S45
Secondary: 22F50 , 55P20 , 55R15 , 55R70

Keywords: completion , connected cover , genus , Localization , Postnikov section , rationalization , self equivalence

Rights: Copyright © 2017 Universitat Autònoma de Barcelona, Departament de Matemàtiques

Vol.61 • No. 1 • 2017
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