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Non-$ G$-equivalent Moore $ G$-spaces of the same type

Author: Ryszard Doman
Journal: Proc. Amer. Math. Soc. 103 (1988), 1317-1321
MSC: Primary 55N25
MathSciNet review: 955029
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Abstract: Let $ G$ be a finite group. By a Moore $ G$-space we mean a $ G$-space $ X$ such that for each subgroup $ H$ of $ G$ the fixed point space $ {X^H}$ is a Moore space of type $ ({M_H},n)$, where $ n > 1$ is a fixed integer and $ {M_H}$ are abelian groups. In this paper it is shown that there exist infinitely many non-$ G$-homotopy equivalent Moore $ G$-spaces of certain given type.

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  • [B] G. E. Bredon, Equivariant cohomology theories, Lecture Notes in Math., vol. 34, Springer-Verlag, Berlin and New York, 1967. MR 0214062 (35:4914)
  • [G-M] P. A. Griffiths and J. W. Morgan, Rational homotopy theory and differential forms, Progress in Math., vol. 16, Birkhäuser, Boston, Mass., 1981. MR 641551 (82m:55014)
  • [H] P. J. Hilton, Homotopy theory and duality, Gordon and Breach, New York, 1965. MR 0198466 (33:6624)
  • [K] P. J. Kahn, Rational Moore $ G$-spaces, Trans. Amer. Math. Soc. 298 (1986), 245-271. MR 857443 (87j:55009)
  • [T] G. V. Triantafillou, Equivariant minimal models, Trans. Amer. Math. Soc. 274 (1982), 509-532. MR 675066 (84g:55017)
  • [W] G. W. Whitehead, Elements of homotopy theory, Graduate Texts in Math., no. 61, Springer-Verlag, Berlin and New York, 1978. MR 516508 (80b:55001)

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Keywords: Moore space, $ G$-CW-complex, $ G$-homotopy equivalence
Article copyright: © Copyright 1988 American Mathematical Society

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