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Transactions of the American Mathematical Society

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ISSN 1088-6850 (online) ISSN 0002-9947 (print)

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An equivariant smash spectral sequence and an unstable box product
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by Michele Intermont PDF
Trans. Amer. Math. Soc. 351 (1999), 2763-2775 Request permission

Abstract:

Let $G$ be a finite group. We construct a first quadrant spectral sequence which converges to the equivariant homotopy groups of the smash product $X \wedge Y$ for suitably connected, based $G$-CW complexes $X$ and $Y$. The $E^2$ term is described in terms of a tensor product functor of equivariant $\Pi$-algebras. A homotopy version of the non-equivariant Künneth theorem and the equivariant suspension theorem of Lewis are both shown to be special cases of the corner of the spectral sequence. We also give a categorical description of this tensor product functor which is analogous to the description in equivariant stable homotopy theory of the box product of Mackey functors. For this reason, the tensor product functor deserves to be called an “unstable box product”.
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Additional Information
  • Michele Intermont
  • Affiliation: Department of Mathematics, Kalamazoo College, Kalamazoo, Michigan 49006
  • Email: intermon@kzoo.edu
  • Received by editor(s): August 18, 1997
  • Published electronically: February 15, 1999
  • © Copyright 1999 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 351 (1999), 2763-2775
  • MSC (1991): Primary 55P91, 55Q91, 55T99, 18G10; Secondary 55P40, 55Q35, 55U25, 18G15, 55U10
  • DOI: https://doi.org/10.1090/S0002-9947-99-02376-4
  • MathSciNet review: 1621753