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Stable homotopy theory is not self-dual


Author: J. M. Boardman
Journal: Proc. Amer. Math. Soc. 26 (1970), 369-370
MSC: Primary 55.40
DOI: https://doi.org/10.1090/S0002-9939-1970-0268887-4
MathSciNet review: 0268887
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Abstract: The classical Spanier-Whitehead duality for finite complexes shows that the finite stable homotopy category is selfdual. We prove that in the larger stable categories, duality is not consistent with the standard arguments of homotopy theory.


References [Enhancements On Off] (What's this?)

  • [1] J. M. Boardman, Stable homotopy theory, University of Warwick, November 1965 (mimeograph).
  • [2] E. H. Spanier, Duality and $ S$-theory, Bull. Amer. Math. Soc. 62 (1956), 194-203. MR 19, 51. MR 0085506 (19:51d)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1970-0268887-4
Keywords: Stable homotopy, Spanier-Whitehead duality, finite spectrum, infinite sum, infinite product
Article copyright: © Copyright 1970 American Mathematical Society

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