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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Some remarks on the structure of Mackey functors


Authors: J. P. C. Greenlees and J. P. May
Journal: Proc. Amer. Math. Soc. 115 (1992), 237-243
MSC: Primary 55M35
MathSciNet review: 1076574
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Abstract | References | Similar Articles | Additional Information

Abstract: All Mackey functors over a finite group $ G$ are built up by short exact sequences from Mackey functors arising from modules over the integral group rings of appropriate subquotients WH of $ G$. The equivariant cohomology theories with coefficients in Mackey functors arising from WH-modules admit particularly simple descriptions.


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

  • [1] Andreas W. M. Dress, Contributions to the theory of induced representations, Algebraic 𝐾-theory, II: “Classical” algebraic 𝐾-theory and connections with arithmetic (Proc. Conf., Battelle Memorial Inst., Seattle, Wash., 1972) Springer, Berlin, 1973, pp. 183–240. Lecture Notes in Math., Vol. 342. MR 0384917 (52 #5787)
  • [2] J. P. C. Greenlees, M. J. Hopkins, and J. P. May, Completions of $ G$-spectra at ideals of the Burnside ring. I, preprint.
  • [3] L. G. Lewis, Jr., The theory of Green functors, mimeographed notes.
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  • [5] J. Thévenaz and P. J. Webb, Simple Mackey functors, Proc. of the 1989 Bressanone Conf. on Group Theory (to appear).

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1992-1076574-2
PII: S 0002-9939(1992)1076574-2
Keywords: Mackey functor, coefficient system, Bredon cohomology, transfer
Article copyright: © Copyright 1992 American Mathematical Society