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POINCARÉ DUALITY FOR K-THEORY OF EQUIVARIANT COMPLEX PROJECTIVE SPACES

Published online by Cambridge University Press:  01 January 2008

J. P. C. GREENLEES
Affiliation:
Department of Pure Mathematics, Hicks Building, Sheffield S3 7RH. UK e-mail: j.greenlees@sheffield.ac.uk
G. R. WILLIAMS
Affiliation:
Department of Pure Mathematics, The Open University, Walton Hall, Milton Keynes, MK7 6AA. UK e-mail: g.r.williams@open.ac.uk
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Abstract

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We make explicit Poincaré duality for the equivariant K-theory of equivariant complex projective spaces. The case of the trivial group provides a new approach to the K-theory orientation [3].

Keywords

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 2008

References

REFERENCES

1.Adams, J. F., Prerequisites (on equivariant stable homotopy) for Carlsson's lecture, in Algebraic topology, Aarhus 1982 Lecture Notes in Mathematics, No. 1051 (Springer-Verlag, 1984), 483–532.Google Scholar
2.Adams, J. F., Lectures on Lie groups (University of Chicago Press, Chicago, IL, 1982). Midway Reprint of the 1969 original.Google Scholar
3.Adams, J. F., Stable homotopy and generalised homology, Chicago Lectures in Mathematics (University of Chicago Press, Chicago, IL, 1995). Reprint of the 1974 original.Google Scholar
4.Bredon, Glen E., Introduction to compact transformation groups (Academic Press, New York, 1972).Google Scholar
5.Cole, Michael, Greenlees, J. P. C. and Kriz, I., The universality of equivariant complex bordism, Math. Z. 239 (3) (2002), 455475.CrossRefGoogle Scholar
6.Costenoble, S. R., May, J. P. and Waner, S., Equivariant orientation theory, in Homology Homotopy Appl., 3 (2) (2001), 265339. Equivariant stable homotopy theory and related areas (Stanford, CA, 2000).CrossRefGoogle Scholar
7.Elmendorf, A. D., Kriz, I., Mandell, M. A. and May, J. P., Rings, modules, and algebras in stable homotopy theory, Mathematical Surveys and Monographs (American Mathematical Society, Providence, RI, 1997).Google Scholar
8.Greenberg, Marvin J. and Harper, John R., Algebraic topology: a first course, Mathematics Lecture Note Series (Addison-Wesley, 1981).Google Scholar
9.Michael, Joachim, Higher coherences for equivariant K-theory, in Structured ring spectra, London Math. Soc. Lecture Note Ser. (Cambridge University Press, 2004), 87114.Google Scholar
10.Lewis, L. G. Jr., and Mandell, Michael A., Equivariant universal coefficient and Künneth spectral sequences, Proc. London Math. Soc. (3) 92 (2) (2006), 505544.CrossRefGoogle Scholar
11.Lewis, L. G. Jr., May, J. P., Steinberger, M. and McClure, J. E., Equivariant stable homotopy theory Lecture Notes in Mathematics. No. 1213 (Springer-Verlag, 1986).CrossRefGoogle Scholar
12.May, J. P., Equivariant homotopy and cohomology theory (CBMS, 1996).Google Scholar
13.Segal, Graeme, Equivariant K-theory. Inst. Hautes Études Sci. Publ. Math. 34 (1968), 129151.CrossRefGoogle Scholar
14.Williams, G. R., Poincaré duality in equivariant K-theory for \C P(V), PhD thesis (University of Sheffield, 2005).Google Scholar