## Publicacions Matemàtiques

### Localization genus

#### 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
Revised: 4 July 2016
First available in Project Euclid: 22 December 2016

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

#### 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