Abstract
Let X be a G-connected nilpotent simplicial set, where G is a finite Hamiltonian group. We construct a cofibrant equivariant minimal model of X with the strong homotopy type of the injective minimal model of X defined by Triantafillou.
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References
Bousfield, A. K. and Guggenheim, V. K. A. M.: On PL de Rham theory and rational homotopy type, Mem. Amer. Math. Soc. 179 (1976).
Golasi?ski, M.: Equivariant rational homotopy theory as a closedmodel category, J. Pure Appl. Algebra 133 (1998), 271–287.
Grove, K., Halperin, S. and Viguè-Poirrier, M.: The rational homotopy theory of certain path-spaces with applications to geodesics, Acta Math. 140 (1978), 277–303.
Hall, M.: The Theory of Groups, Macmillan, New York, 1962.
Halperin, S.: Lectures on minimal models, Mèm. Soc. Math. France (N.S.) 9–10 (1983).
Lambre, T.: Modèle pour les Zp-espace, Thèse, Lille (1987).
Lambre, T.: Modèle minimal équivariant et formalité, Trans. Amer. Math. Soc. 327 (1991), 621–639.
Lück, W.: Transformation Groups and Algebraic K-theory, Lecture Notes in Math. 1408, Springer-Verlag, New York, 1989.
Oprea, J. F.: Lifting homotopy actions in rational homotopy theory, J. Pure Appl. Algebra 32 (1984), 177–190.
Quillen, D. G.: Homotopical Algebra, Lecture Notes in Math. 43, Springer-Verlag, New York, 1967.
Sullivan, D.: Infinitesimal computations in topology, Publ. Inst. Haute Etudes Sci. 47 (1977).
Tanré, D.: Homotopie rationnelle modèles de Chen, Quillen, Sullivan, Lecture Notes in Math. 1025, Springer-Verlag, New York, 1983.
Triantafillou, G. V.: Äquivariante rationale Homotopietheorie, Bonner Math. Schriften 110, Univ. Bonn, Bonn, 1978.
Triantafillou, G. V.: Equivariant minimal models, Trans. Amer. Math. Soc. 274 (1982), 509–532.
Triantafillou, G. V.: An algebraic model for G-homotopy types, Astèrisque 113–114 (1984), 312-337.
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Golasiński, M. On Injective and Cofibrant Equivariant Minimal Models. Compositio Mathematica 124, 1–9 (2000). https://doi.org/10.1023/A:1002435421823
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DOI: https://doi.org/10.1023/A:1002435421823