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- W2095250635 abstract "For any finite simplicial complex K, Davis and Januszkiewiczhave 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 problemrationally 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 theStanley-Reisner algebra is a complete intersection." @default.
- W2095250635 created "2016-06-24" @default.
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- W2095250635 date "2010-08-29" @default.
- W2095250635 modified "2023-10-17" @default.
- W2095250635 title "On Davis–Januszkiewicz homotopy types II: Completion and globalisation" @default.
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- W2095250635 doi "https://doi.org/10.2140/agt.2010.10.1747" @default.
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