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research article

Cellular properties of nilpotent spaces

Chacholski, Wojciech
•
Farjoun, Emmanuel Dror
•
Flores, Ramon
Show more
2015
Geometry & Topology

We show that cellular approximations of nilpotent Postnikov stages are always nilpotent Postnikov stages, in particular classifying spaces of nilpotent groups are turned into classifying spaces of nilpotent groups. We use a modified Bousfield-Kan homology completion tower z(k) X whose terms we prove are all X-cellular for any X. As straightforward consequences, we show that if X is K-acyclic and nilpotent for a given homology theory K, then so are all its Postnikov sections P-n X, and that any nilpotent space for which the space of pointed self-maps map(*) (X, X) is "canonically" discrete must be aspherical.

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Type
research article
DOI
10.2140/gt.2015.19.2741
Web of Science ID

WOS:000365637300007

Author(s)
Chacholski, Wojciech
Farjoun, Emmanuel Dror
Flores, Ramon
Scherer, Jerome
Date Issued

2015

Publisher

Geometry & Topology Publications

Published in
Geometry & Topology
Volume

19

Issue

5

Start page

2741

End page

2766

Editorial or Peer reviewed

REVIEWED

Written at

EPFL

EPFL units
UPHESS  
Available on Infoscience
February 16, 2016
Use this identifier to reference this record
https://infoscience.epfl.ch/handle/20.500.14299/123658
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