A Functor Converting Equivariant Homology to Homotopy
نویسنده
چکیده
In this paper, an equivariant version of the classical Dold-Thom theorem is proved. Let G be a finite group, X a G-space, and k a covariant coefficient system on G. Then a topological abelian group GX ⊗GF k is constructed by the coend construction. For a G-CW complex X, it is proved that there is a natural isomorphism πi(GX ⊗GF k) ∼= H G i (X; k), where the right hand side is the Bredon equivariant homology of X with coefficients in k. At the end, several examples of this result are presented.
منابع مشابه
Functor Converting Equivariant Homology to Homotopy
In this paper, we prove an equivariant version of the classical Dold-Thom theorem. Let G be a finite group, X a G-space, and k a covariant coefficient system on G. We construct a topological abelian group GX ⊗ G k by the coend construction. We then prove that for a G-CW complex X, πi(GX⊗ B G k) ∼= H i (X; k), where the right hand side is the Bredon equivariant homology of X with coefficients in...
متن کاملThe Equivariant Dold-thom Theorem
(1) A. Dold, R. Thom, Quasifaserungen und unendliche symmetrische produkte, Ann. of Math. (2) 67 (1958), 239–281. (2) E. Spanier, Infinite symmetric products, function spaces, and duality, Ann. of Math. (2) 69 (1959), 142–198. (3) M. C. McCord, Classifying spaces and infinite symmetric products, Trans. Amer. Math. Soc. 146 (1969), 273–298. (4) M. G. Barratt, S. Priddy, On the homology of non-co...
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