The Adams spectral sequence
Authors:
Wolfgang Lellmann and Mark Mahowald
Journal:
Trans. Amer. Math. Soc. 300 (1987), 593623
MSC:
Primary 55T15; Secondary 55N15, 55Q45, 55S25
MathSciNet review:
876468
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Abstract: Due to its relation to the image of the homomorphism and first order periodicity (Bott periodicity), connective real theory is well suited for problems in local stable homotopy that arise geometrically. On the other hand the use of generalized homology theories in the construction of Adams type spectral sequences has proved to be quite fruitful provided one is able to get a hold on the respective terms. In this paper we make a first attempt to construct an algebraic and computational theory of the term of the boAdams spectral sequence. This allows for some concrete computations which are then used to give a proof of the bounded torsion theorem of [8] as used in the geometric application of [2]. The final table of the term for in shows that the statement of this theorem cannot be improved. No higher differentials appear in this range of the boAdams spectral sequence. We observe, however, that such a differential has to exist in dim 30.
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 J. F. Adams, Stable homotopy and generalized homology, University Press, Chicago, 1974. MR 0402720 (53:6534)
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 , Correction to The stable geometric dimension of vector bundles over real projective spaces, Trans. Amer. Math. Soc. 280 (1983), 841843. MR 716854 (85g:55006)
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 W. Lellmann, Operations and cooperations in oddprimary connective theory, J. London Math. Soc. (2) 29 (1984), 562576. MR 754942 (88a:55020)
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 , The term of the Adams Spectral sequence based on connected Morava theory, preprint.
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 , bo resolutions, Pacific J. Math. 92 (1981), 365383. MR 618072 (82m:55017)
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 , An addendum to boresolutions, Pacific J. Math. 111 (1984), 117123. MR 732062 (86a:55018)
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 , The image of in the EHPsequence, Ann. of Math. (2)116 (1982), 65112. MR 662118 (83i:55019)
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 H. R. Margolis, EilenbergMac Lane spectra, Proc. Amer. Math. Soc. 43 (1974), 409415. MR 0341488 (49:6239)
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 R. J. Milgram, The Steenrod algebra and its dual for connective theory, Reunion sobre homotopia, Northwestern Univ., 1974 (Sociedad Matematica Mexicana, 1975), pp. 127158. MR 761725
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 H. R. Miller, On relations between Adams spectral sequences with an application to the stable homotopy of the Moore space, J. Pure Appl. Algebra 20 (1981), 187312. MR 604321 (82f:55029)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947198708764681
PII:
S 00029947(1987)08764681
Keywords:
Connective theory,
Adams spectral sequences,
stable homotopy groups,
theory operations,
filtration spectral sequences
Article copyright:
© Copyright 1987
American Mathematical Society
