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BSJ does not map correctly into BSF mod 2

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Abstract

Let BSJ denote the “quotient” of\(BSO\xrightarrow{{\psi ^3 - 1}}BSO\) localized at 2. It had been thought that the Adams conjecture might deloop to give a diagram

realizing the J-homomorphism. We show this to be impossible by showing there do not exist Stiefel-Whitnev class Wn (even for n≤13) in BSJ satisfving the Wu formulas.

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References

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Authors and Affiliations

  1. Mathematics Department, University of Notre Dame, 46556, Notre Dame, Indiana

    Robert R. Clough

  2. Mathematics Department, Temple University, 19122, Philadelphia, Pennsylvania

    James D. Stasheff

Authors
  1. Robert R. Clough
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  2. James D. Stasheff
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Additional information

The result of the title also follows from independent and earlier work of Ib Madsen who showed that there is no H-map of SO into F/0 which is correct on homotopy. Apparently the same methods apply to SJ into SF. It is not clear to us how the obstructions compare.

Research supported in part by NSF grant GP-29660.

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Clough, R.R., Stasheff, J.D. BSJ does not map correctly into BSF mod 2. Manuscripta Math 7, 205–214 (1972). https://doi.org/10.1007/BF01579720

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  • DOI: https://doi.org/10.1007/BF01579720

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