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Cellular properties of
nilpotent spaces
Wojciech Chachólski, Emmanuel Dror Farjoun, Ramón Flores and Jérôme Scherer |
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Geometry & Topology 19 (2015) 2741–2766
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Abstract |
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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 whose terms we prove are all –cellular for any . As straightforward consequences, we show that if is –acyclic and nilpotent for a given homology theory , then so are all its Postnikov sections , and that any nilpotent space for which the space of pointed self-maps is “canonically” discrete must be aspherical. |
Keywords
cellular approximation, nilpotent group, generalized
homology theory, classifying spaces of groups,
Eilenberg–Mac Lane space
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Mathematical Subject Classification 2010
Primary: 55P60, 20F18
Secondary: 55N20, 55R35
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References |
Publication
Received: 16 January 2014
Revised: 8 October 2014
Accepted: 12 November 2014
Published: 20 October 2015
Proposed: Mark Behrens
Seconded: Haynes Miller, Jesper Grodal
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Authors |
| Wojciech Chachólski | |
| Department of Mathematics KTH Stockholm Lindstedtsvägen 25 10044 Stockholm Sweden |
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| Emmanuel Dror Farjoun | |
| Department of Mathematics Hebrew University of Jerusalem Givat Ram Jerusalem 91904 Israel |
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| Ramón Flores | |
| Departamento de Matemáticas Facultad de Ciencias Universidad Autónoma de Madrid 28049 Madrid Spain |
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| Jérôme Scherer | |
| Department of Mathematics EPFL Lausanne Station 8 1015 Lausanne Switzerland |
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| http://gr-he.epfl.ch/Scherer | |
