Effective homology for homotopy colimit and cofibrant replacement

Filakovský, Marek

Archivum mathematicum, Tome 50 (2014) no. 5, pp. 273-286

Abstract (VO)

We extend the notion of simplicial set with effective homology presented in [22] to diagrams of simplicial sets. Further, for a given finite diagram of simplicial sets $X \colon \mathcal{I}\rightarrow \mbox{sSet}$ such that each simplicial set $X(i)$ has effective homology, we present an algorithm computing the homotopy colimit $\mbox{hocolim}\,X$ as a simplicial set with effective homology. We also give an algorithm computing the cofibrant replacement $X^{\mbox{cof}}$ of $X$ as a diagram with effective homology. This is applied to computing of equivariant cohomology operations.

Détail

DOI : 10.5817/AM2014-5-273

Classification : 55N91, 55U15
Keywords: homotopy colimit; cofibrant replacement; effective homology; equivariant

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