On the realization of invariant subgroups of
Author:
A. Zabrodsky
Journal:
Trans. Amer. Math. Soc. 285 (1984), 467496
MSC:
Primary 55Q52; Secondary 55P45, 55S45
MathSciNet review:
752487
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Abstract: Let be a prime and a self map. Let be a multiplicatively closed subset of the algebraic closure of . Denote by the set of characteristic values of lying in . It is proved that under certain conditions is realizable by a pair : There exist a space , maps and so that is injective and . This theorem yields, among others, examples of spaces whose cohomology rings are polynomial algebras.
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 [A]
 Clark and J. Ewing, The realization of polynomial algebras as cohomology rings, Pacific J. Math. 50 (1974), 425434. MR 0367979 (51:4221)
 [G]
 E. Cooke, Constructing spaces with interesting cohomology via actions on loop spaces, Amer. J. Math. 103 (1979), 515542. MR 533189 (80m:57032)
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 G E. Cooke and L. Smith, Decomposition of cospaces and applications, Math. Z. 157 (1977), 155157. MR 0478145 (57:17634)
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 Freyd, Stable homotopy, Proc. Conf. on Categorical Algebra (La Jolla), SpringerVerlag, Berlin, 1966. MR 0211399 (35:2280)
 [E]
 M. Friedlander, Exceptional isogenies and the classifying spaces of simple Lie groups, Ann. of Math. (2) 101 (1975), 510520. MR 0391078 (52:11900)
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 Harper, spaces with torsion, Mem. Amer. Math. Soc. No. 22 (1979). MR 546361 (80k:55033)
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 Nishida, On a result of Sullivan and the decomposition of Lie groups, Mimeographed Notes, Research Inst. for Math. Sci., Kyoto Univ., 1971.
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 Quillen, On the cohomology and theory of the general linear group over a finite field, Ann. of Math. (2) 96 (1972), 552586. MR 0315016 (47:3565)
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 Stasheff, decomposition of Lie groups, Localization in Group Theory and Homotopy Theory, Lecture Notes in Math., vol. 418, SpringerVerlag, Berlin and New York, 1974, pp.142149. MR 0375294 (51:11490)
 [D]
 Sullivan, Geometric topology, Mimeographed Notes, M.I.T., 1971.
 [C]
 Wilkerson, 1. Genus and cancellation, Topology 17 (1975), 2936. MR 0367995 (51:4237)
 2.
 , 2. Self maps of classifying spaces, Localization in Group Theory and Homotopy Theory, Lecture Notes in Math., vol. 418, SpringerVerlag, Berlin and New York, 1974, pp.150157. MR 0383444 (52:4325)
 [A]
 Zabrodsky, 1. Endomorphisms in the homotopy category, Mimeographed Notes.
 3.
 , 2. equivalence and homotopy types, Localization in Group Theory and Homotopy Theory, Lecture Notes in Math., vol. 418, SpringerVerlag, Berlin and New York, 1974, pp.161171. MR 0377867 (51:14036)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947198407524878
PII:
S 00029947(1984)07524878
Article copyright:
© Copyright 1984
American Mathematical Society
