Abstract
We present a variant of the disconnected equivariant rational homotopy theory to complete the result shown in [8]. For a finite group G let O(G) be the category of its canonical orbits. We prove that the category O(G)∫-DGA ∧ Q of O(G)∫S-complete differential graded algebras over the rationals is a closed model category, where S runs over all O(G)-sets. Then, by means of the equivariant KS-minimal models, we show that the homotopy category of O(G)∫-DGA ∧ Q is equivalent to the rational homotopy category of G-nilpotent disconnected simplicial sets provided G is a finite Hamiltonian group.
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Golasiński, M. Disconnected Equivariant Rational Homotopy Theory. Applied Categorical Structures 10, 23–33 (2002). https://doi.org/10.1023/A:1013368802522
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DOI: https://doi.org/10.1023/A:1013368802522