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Moore G-Spaces Which are not Co-Hopf G-Spaces

Part of: Homotopy theory

Published online by Cambridge University Press:  20 November 2018

Ryszard Doman
Ryszard Doman*
Affiliation:
Institute of Mathematics A. Mickiewicz University Matejki 48/49 60-769 Poznań, Poland
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Abstract

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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 XH is a simply connected Moore space of type (MH,n), where MH is an abelian group depending on H, and n is a fixed integer. By a co-Hopf G-space we mean a G-space with a G-equivariant comultiplication. In this note it is shown that, in contrast to the non-equivariant case, there exist Moore G-spaces which are not co-Hopf G-spaces.

MSC classification

Secondary: 55P99: None of the above, but in this section 57S17: Finite transformation groups
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 32 , Issue 3 , 01 September 1989 , pp. 365 - 368
Copyright
Copyright © Canadian Mathematical Society 1989

References

1. Bredon, G. E., Equivariant Cohomology Theories, Lecture Notes in Math. vol. 34, Springer-Verlag, Berlin-Heidelberg-New York, 1967.Google Scholar
2. Doman, R., Non G-equivalent Moore G-spaces of the same type, Proc. Amer. Math. Soc. 103 (1988), pp. 1317–1321.Google Scholar
3. Hilton, P., Homotopy Theory and Duality, Gordon and Breach, New York, 1965.Google Scholar
4. Kahn, P. J., Rational Moore G-spaces, Trans. Amer. Math. Soc. 298 (1986), pp. 245–271.Google Scholar
5. Triantafillou, G. V., Equivariant minimal models, Trans. Amer. Math. Soc. 274 (1982), pp. 509–532.Google Scholar
6. Whitehead, G. W., Elements of Homotopy Theory, Springer-Verlag, New York-Heidelberg-Berlin, 1978.Google Scholar