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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

An equivariant smash spectral sequence
and an unstable box product


Author: Michele Intermont
Journal: Trans. Amer. Math. Soc. 351 (1999), 2763-2775
MSC (1991): Primary 55P91, 55Q91, 55T99, 18G10; Secondary 55P40, 55Q35, 55U25, 18G15, 55U10
Published electronically: February 15, 1999
MathSciNet review: 1621753
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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

DOI: http://dx.doi.org/10.1090/S0002-9947-99-02376-4
PII: S 0002-9947(99)02376-4
Keywords: Smash product, box product, tensor product functor, equivariant spectral sequence, Kan extension, K\"unneth theorem, Freudenthal suspension theorem, equivariant homotopy theory
Received by editor(s): August 18, 1997
Published electronically: February 15, 1999
Article copyright: © Copyright 1999 American Mathematical Society