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On the notion of residual finiteness for G-spaces

Part of: Homotopy theory

Published online by Cambridge University Press:  09 April 2009

Goutam Mukherjee  and
Aniruddha C. Naolekar
Aniruddha C. Naolekar
Affiliation:
Stat.-Math. Unit, Indian Statistical Institute, 203, B. T. Road, Calcutta 700035, India e-mail: [email protected], [email protected]
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Abstract

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We define equivariant completion of a G-complex and define residually finite G-spaces. We show that the group of G-homotopy classes of G-homotopy self equivalences of a finite, residually finite G-complex, in residually finite. This generalizes some results of Roitberg.

Keywords

equivariant completionresidually finite G-spacesresidually finite groupsHopfian groups

MSC classification

Secondary: 55P60: Localization and completion 57S17: Finite transformation groups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 73 , Issue 3 , December 2002 , pp. 347 - 356
Copyright
Copyright © Australian Mathematical Society 2002

References

[1]Bredon, G. E., Equivariant cohomology theories, Lecture Notes in Math. 34 (Springer, Berlin, 1967).Google Scholar
[2]Elmendorf, A. D.. ‘Systems of fixed point sets’, Trans. Amer Math. Soc. 277 (1983), 275–284.CrossRefGoogle Scholar
[3]May, J. P., ‘Equivariant completion’, Bull. London Math. Soc. 14 (1982), 231–237.CrossRefGoogle Scholar
[4]May, J. P., Equivariant homotopy and cohomology theory, CBMS Regional Conf. Series in Math. 91 (Amer. Math. Soc., Providence, 1996).CrossRefGoogle Scholar
[5]Mukherjee, A. and Mukherjee, G., ‘Bredon-Illman cohomology with local coefficients’, Quart. J. Math. Oxford (2) 47 (1996), 199–219.CrossRefGoogle Scholar
[6]Mukherjee, G., ‘Hopfian and co-Hopfian G-CW-complexes’, Proc. Amer. Math. Soc. 125 (1997), 1229–1236.CrossRefGoogle Scholar
[7]Roitberg, J., ‘Residual finiteness in homotopy theory’, J. Pure Appl. Algebra 32 (1984), 347–358.CrossRefGoogle Scholar
[8]Sullivan, D., ‘Genetics of homotopy theory and the Adams conjecture’, Ann. of Math. (2) 100 (1974), 1–79.CrossRefGoogle Scholar
[9]Sullivan, D., ‘Infinitesimal computations in topology’, Pubi. Inst. Haute Etude Sci. 47 (1978), 269–331.CrossRefGoogle Scholar
[10]Triantafihlou, G., ‘An algebraic model for G-homotopy types’, Asrérisque 113–114 (1984), 312–337.Google Scholar
[11]Wilkerson, C. W., ‘Applications of minimal simplicial groups’, Topology 15 (1976), 111–130.CrossRefGoogle Scholar