On Davis-Januszkiewicz homotopy types I: formality and rationalisation. (English) Zbl 1065.55006
Let \(K\) be a simplicial complex. Davis and Januszkiewicz have defined a CW complex whose integral cohomology ring is isomorphic to the Stanley-Reisner algebra of \(K\). Subsequently, Buchstaber and Panov gave an alternative description, denoted here by \(c(K)\). In fact, \(c(K)\) is the colimit of the diagram whose objects are the \(K(\mathbb{Z}, 2)^{\dim\sigma}\) with \(\sigma\in K\) and the arrows correspond to the injections of simplices. The authors make a study of this space in terms of model category theory. They prove that the space is formal over the integers and also in rational homotopy.
Reviewer: Yves Félix (Louvain-La-Neuve)
MSC:
| 55P62 | Rational homotopy theory |
| 55U05 | Abstract complexes in algebraic topology |
| 05E99 | Algebraic combinatorics |
Keywords:
colimit; formality; homotopy colimit; model category; rational homotopy; Stanley-Reisner algebraReferences:
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