An integral version of the BrownGitler spectrum
Author:
Don H. Shimamoto
Journal:
Trans. Amer. Math. Soc. 283 (1984), 383421
MSC:
Primary 55P42; Secondary 55P35, 55S10, 55S45, 57R19
MathSciNet review:
737876
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Abstract: In this paper, certain spectra are studied whose behavior qualifies them as being integral versions of the BrownGitler spectra . The bulk of our work emphasizes the similarities between and , shown mainly using the techniques of Brown and Gitler. In analyzing the homotopy type of , we provide a free resolution over the Steenrod algebra for its cohomology and study its Adams spectral sequence. We also list conditions which characterize it at the prime . The paper begins, however, on a somewhat different topic, namely, the construction of a configuration space model for and other related spaces.
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 A. K. Bousfield and D. M. Kan, Homotopy limits, completions and localizations, Lecture Notes in Math., vol. 304, SpringerVerlag, New York, 1972. MR 0365573 (51:1825)
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 E. H. Brown, Jr., and S. Gitler, A spectrum whose cohomology is a certain cyclic module over the Steenrod algebra, Topology 12 (1973), 283295. MR 0391071 (52:11893)
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 , Relations among characteristic classes. I, Topology 3 (1964), 3952. MR 0163326 (29:629)
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 , On the stable decomposition of , Trans. Amer. Math. Soc. 243 (1978), 287298. MR 0500933 (58:18424)
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 F. R. Cohen, T. J. Lada and J. P. May, The homology of iterated loop spaces, Lecture Notes in Math., vol. 533, SpringerVerlag. New York, 1976. MR 0436146 (55:9096)
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 F. R. Cohen, J. P. May and L. R. Taylor, and as Thom spectra, Illinois J. Math. 25 (1981), 99106. MR 602900 (82h:55008)
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 R. L. Cohen, The geometry of and braid orientations, Invent. Math. 54 (1979), 5367. MR 549545 (81a:55013)
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 D. M. Davis, S. Gitler and M. Mahowald, The stable geometric dimension of vector bundles over real projective spaces, Trans. Amer. Math. Soc. 268 (1981), 3961. MR 628445 (83c:55006)
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 P. Goerss, Results on BrownGitler type spectra, Ph. D. Dissertation, M. I. T., 1983.
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 M. Mahowald, resolutions, Pacific J. Math. 92 (1981), 365383. MR 618072 (82m:55017)
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 , A new infinite family in , Topology 16 (1977), 249256. MR 0445498 (56:3838)
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 , Ring spectra which are Thom complexes, Duke Math. J. 46 (1979), 549559. MR 544245 (81f:55010)
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 J. P. May, The geometry of iterated loop spaces, Lecture Notes in Math., vol. 271, SpringerVerlag, New York, 1972. MR 0420610 (54:8623b)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002994719840737876X
PII:
S 00029947(1984)0737876X
Keywords:
BrownGitler spectrum,
Steenrod algebra,
iterated loop space,
Thom spectrum,
algebra,
Adams spectral sequence,
orientability of manifolds,
Postnikov tower
Article copyright:
© Copyright 1984
American Mathematical Society
