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Nilpotence and finite H-spaces

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Abstract

Zabrodsky asked when is the iterated commutator mapX n →X for a connected associative H-spaceX a null map. In this paper we reduce this question to a cohomological question and answer it in several cases.

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References

  1. E. Devinatz, M. J. Hopkins and J. H. Smith,Nilpotence and stable homotopy theory I, Ann. of Math.128 (1988), 207–241.

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  2. M. J. Hopkins and J. H. Smith,Nilpotence and stable homotopy theory II, to appear.

  3. D. C. Ravenel,Complex Cobordism and Stable Homotopy Groups of Spheres, Academic Press, New York, 1986.

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  4. A. Zabrodsky,Hopf Spaces, North-Holland Math. Studies 22, North-Holland, Amsterdam, 1976.

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Authors and Affiliations

  1. Department of Mathematics, The University of Chicago, Chicago, Illinois, USA

    Michael J. Hopkins

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  1. Michael J. Hopkins
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Supported by an NSF Presidential Young Investigator award and the Sloan Foundation.

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Hopkins, M.J. Nilpotence and finite H-spaces. Israel J. Math. 66, 238–246 (1989). https://doi.org/10.1007/BF02765895

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  • DOI: https://doi.org/10.1007/BF02765895

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