A nonexistence result for Moore $G$-spectra
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- by S. R. Costenoble and S. Waner PDF
- Proc. Amer. Math. Soc. 113 (1991), 265-274 Request permission
Abstract:
In this paper we show that certain equivariant Moore spectra do not exist. Specifically, we give an example of a Bredon coefficient system for which there is no corresponding equivariant Moore CW-spectrum that is bounded below. This nonexistence result is stronger than nonexistence results shown previously; nonexistence of an equivariant Moore spectrum of type $T$ implies, in particular, that there are no equivariant Moore spaces of type $(T,n)$ for any $n$. As a key step, we show that there is no strictly commutative Hopf space structure on the loop space $Q{S^0}$ agreeing up to infinite loop homotopy with the usual addition.References
- Glen E. Bredon, Equivariant cohomology theories, Lecture Notes in Mathematics, No. 34, Springer-Verlag, Berlin-New York, 1967. MR 0214062, DOI 10.1007/BFb0082690
- J. Caruso and S. Waner, An approximation to $\Omega ^{n}\Sigma ^{n}X$, Trans. Amer. Math. Soc. 265 (1981), no. 1, 147–162. MR 607113, DOI 10.1090/S0002-9947-1981-0607113-2
- Peter J. Kahn, Rational Moore $G$-spaces, Trans. Amer. Math. Soc. 298 (1986), no. 1, 245–271. MR 857443, DOI 10.1090/S0002-9947-1986-0857443-9
- L. G. Lewis Jr., J. P. May, M. Steinberger, and J. E. McClure, Equivariant stable homotopy theory, Lecture Notes in Mathematics, vol. 1213, Springer-Verlag, Berlin, 1986. With contributions by J. E. McClure. MR 866482, DOI 10.1007/BFb0075778
- J. M. Boardman and R. M. Vogt, Homotopy invariant algebraic structures on topological spaces, Lecture Notes in Mathematics, Vol. 347, Springer-Verlag, Berlin-New York, 1973. MR 0420609, DOI 10.1007/BFb0068547 —, ${E^\infty }$ ring spaces and ${E^\infty }$ ring spectra and their applications, Lecture Notes in Math., vol. 577, Springer-Verlag, Berlin and New York, 1977.
- John C. Moore, Semi-simplicial complexes and Postnikov systems, Symposium internacional de topología algebraica International symposium on algebraic topology, Universidad Nacional Autónoma de México and UNESCO, Mexico City, 1958, pp. 232–247. MR 0111027 G. Triantafillou, $G$-spaces with prescribed equivariant cohomology, Univ. of Minnesota, preprint.
Additional Information
- © Copyright 1991 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 113 (1991), 265-274
- MSC: Primary 55N91; Secondary 55P47, 55P91
- DOI: https://doi.org/10.1090/S0002-9939-1991-1041013-3
- MathSciNet review: 1041013