Document Zbl 0594.55020 - zbMATH Open

It is shown that the category of cyclic sets of A. Connes [C. R. Acad. Sci., Paris, Sér. I 296, 953-958 (1983; Zbl 0534.18009)] admits the structure of a closed model category and that the resulting homotopy theory is equivalent to the homotopy theory of SO(2) spaces as well as to that of simplicial sets over K(\({\mathbb{Z}},2)\). Moreover, the first and last of these results hold more generally; e.g. the homotopy theory of bG spaces (where bG is the flattening of the simplicial group G as defined by the first and third authors [J. Pure Appl. Algebra 35, 269-285 (1985; Zbl 0567.55010)] is equivalent to the homotopy theory of simplicial sets over the classifying complex of G.

MSC:

55U35	Abstract and axiomatic homotopy theory in algebraic topology
55U10	Simplicial sets and complexes in algebraic topology
55R35	Classifying spaces of groups and \(H\)-spaces in algebraic topology
55P99	Homotopy theory
18G30	Simplicial sets; simplicial objects in a category (MSC2010)

References:

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