Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-24T06:13:00.905Z Has data issue: false hasContentIssue false

On the notion of residual finiteness for G-spaces

Published online by Cambridge University Press:  09 April 2009

Aniruddha C. Naolekar
Affiliation:
Stat.-Math. Unit, Indian Statistical Institute, 203, B. T. Road, Calcutta 700035, India e-mail: [email protected], [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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.

Type
Research Article
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), 275284.CrossRefGoogle Scholar
[3]May, J. P., ‘Equivariant completion’, Bull. London Math. Soc. 14 (1982), 231237.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), 199219.CrossRefGoogle Scholar
[6]Mukherjee, G., ‘Hopfian and co-Hopfian G-CW-complexes’, Proc. Amer. Math. Soc. 125 (1997), 12291236.CrossRefGoogle Scholar
[7]Roitberg, J., ‘Residual finiteness in homotopy theory’, J. Pure Appl. Algebra 32 (1984), 347358.CrossRefGoogle Scholar
[8]Sullivan, D., ‘Genetics of homotopy theory and the Adams conjecture’, Ann. of Math. (2) 100 (1974), 179.CrossRefGoogle Scholar
[9]Sullivan, D., ‘Infinitesimal computations in topology’, Pubi. Inst. Haute Etude Sci. 47 (1978), 269331.CrossRefGoogle Scholar
[10]Triantafihlou, G., ‘An algebraic model for G-homotopy types’, Asrérisque 113–114 (1984), 312337.Google Scholar
[11]Wilkerson, C. W., ‘Applications of minimal simplicial groups’, Topology 15 (1976), 111130.CrossRefGoogle Scholar