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Characterisation of polyhedral products with finite generalised Postnikov decomposition
- Source :
- Forum Mathematicum. 32:1253-1269
- Publication Year :
- 2020
- Publisher :
- Walter de Gruyter GmbH, 2020.
-
Abstract
- A generalised Postnikov tower for a space $X$ is a tower of principal fibrations with fibres generalised Eilenberg-MacLane spaces, whose inverse limit is weakly homotopy equivalent to $X$. In this paper we give a characterisation of a polyhedral product $Z_K(X,A)$ whose universal cover either admits a generalised Postnikov tower of finite length, or is a homotopy retract of a space admitting such a tower. We also include $p$-local and rational versions of the theorem. We end with a group theoretic application.<br />24 pages
- Subjects :
- Homotopy group
Pure mathematics
Group (mathematics)
Covering space
Applied Mathematics
General Mathematics
Homotopy
010102 general mathematics
55S45, 55P15, 20F36
Space (mathematics)
Mathematics::Algebraic Topology
01 natural sciences
Tower (mathematics)
010101 applied mathematics
Mathematics::K-Theory and Homology
Mathematics::Category Theory
Retract
FOS: Mathematics
Algebraic Topology (math.AT)
Mathematics - Algebraic Topology
Inverse limit
0101 mathematics
Mathematics
Subjects
Details
- ISSN :
- 14355337 and 09337741
- Volume :
- 32
- Database :
- OpenAIRE
- Journal :
- Forum Mathematicum
- Accession number :
- edsair.doi.dedup.....ebcb2bbfe266fb0a68281f600272da8b