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CW decompositions of equivariant CW complexes

Published online by Cambridge University Press:  17 April 2009

M. Cencelj  and
N. Mramor Kosta
M. Cencelj
Affiliation:
Institute of Mathematics, Physics and Mechanics, Faculty of Computer and Information Science and Faculty of Education, University of Ljubljana, Jadranska 19, SI-1000 Ljublijana, Slovenia e-mail: neza.mramor-kosta@fmf.uni-lj.simatija.cencelj@fmf.uni-lj.si
N. Mramor Kosta
Affiliation:
Institute of Mathematics, Physics and Mechanics, Faculty of Computer and Information Science and Faculty of Education, University of Ljubljana, Jadranska 19, SI-1000 Ljublijana, Slovenia e-mail: neza.mramor-kosta@fmf.uni-lj.simatija.cencelj@fmf.uni-lj.si
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Abstract

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we discuss conditions which ensure that a G-CW complex is G-homotopy equivalent to a CW complex with cellular action with respect to some CW decomposition of the compact Lie group G. For G = SU (2), we prove that for every G-CW complex X, there exists a CW complex Y which is G-homotopy equivalent to X, such that the action G × Y → Y is a cellular map.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 65 , Issue 1 , February 2002 , pp. 45 - 53
Copyright
Copyright © Australian Mathematical Society 2002

References

[1]Greenlees, J.P.C. and May, J.P., Generalized Tate cohomology, Memoirs Amer. Math. Soc. 113 (American Mathematical Society, Providence, R.I., 1995).Google Scholar
[2]Hsiang, W.Y., Cohomology theory of topological transformation groups (Springer-Verlag, Berlin Heidelberg New York, 1975).CrossRefGoogle Scholar
[3]Illman, S., ‘Equivariant singular homology and cohomology for actions of compact Lie groups’,in Proceedings of the Second Conference on Compact Transformation Groups, Univ. of Massachusetts,Amherst,1971, Lecture Notes in Math. Vol. 298 (Springer-Verlag, Berlin, Heidelberg, New York, 1972), pp. 403–415.CrossRefGoogle Scholar
[4]Illman, S., ‘Restricting the transformation group in equivariant CW complexes’, Osaka J. Math. 27 (1990), 191–206.Google Scholar
[5]Matumoto, T., ‘On G-CW complexes and a theorem of J.H.C. Whitehead’, J. Fac. Sci. Univ. Tokyo Sect. 1A Math. 18 (1971), 109–125.Google Scholar
[6]Munkres, J.R., Elementary differential topology, Annals of Mathematical Studies 54 (Princeton University Press, Princeton, New Jersey, 1966).Google Scholar
[7]Pérez, J.A., ‘Substitutional lemma for G-spaces of 1-dimensional groups’, Glasgow Math. J. 38 (1996), 215–220.CrossRefGoogle Scholar
[8]Suzuki, I., Group Theory I (Springer-Verlag, Berlin, Heidelberg, New York, 1982).CrossRefGoogle Scholar
[9]tom Dieck, T., Transformation groups (Walter de Gruyter, Berlin, New York, 1987).CrossRefGoogle Scholar
[10]tom Dieck, T., Transformation groups and representation theory, Lecture Notes in Mathematics 766 (Springer-Verlag, Berlin, Heidelberg, New York, 1979).CrossRefGoogle Scholar