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2010 On Davis–Januszkiewicz homotopy types {II}: {C}ompletion and globalisation
Dietrich Notbohm, Nigel Ray
Algebr. Geom. Topol. 10(3): 1747-1780 (2010). DOI: 10.2140/agt.2010.10.1747

Abstract

For any finite simplicial complex K, Davis and Januszkiewicz defined a family of homotopy equivalent CW–complexes whose integral cohomology rings are isomorphic to the Stanley–Reisner algebra of K. Subsequently, Buchstaber and Panov gave an alternative construction, which they showed to be homotopy equivalent to the original examples. It is therefore natural to investigate the extent to which the homotopy type of a space X is determined by such a cohomology ring. Having analysed this problem rationally in Part I, we here consider it prime by prime, and utilise Lannes’ T–functor and Bousfield–Kan type obstruction theory to study the p–completion of X. We find the situation to be more subtle than for rationalisation, and confirm the uniqueness of the completion whenever K is a join of skeleta of simplices. We apply our results to the global problem by appealing to Sullivan’s arithmetic square, and deduce integral uniqueness whenever the Stanley–Reisner algebra is a complete intersection.

Citation

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Dietrich Notbohm. Nigel Ray. "On Davis–Januszkiewicz homotopy types {II}: {C}ompletion and globalisation." Algebr. Geom. Topol. 10 (3) 1747 - 1780, 2010. https://doi.org/10.2140/agt.2010.10.1747

Information

Received: 16 December 2008; Revised: 8 April 2009; Accepted: 11 April 2009; Published: 2010
First available in Project Euclid: 19 December 2017

zbMATH: 1198.55005
MathSciNet: MR2683752
Digital Object Identifier: 10.2140/agt.2010.10.1747

Subjects:
Primary: 55P15, 55P60
Secondary: 05E99

Rights: Copyright © 2010 Mathematical Sciences Publishers

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