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A Mapping Problem and Jp-Index. I

Published online by Cambridge University Press:  20 November 2018

Masami Wakae  and
Oma Hamara
Masami Wakae
Affiliation:
University of Manitoba, Winnipeg, Manitoba
Oma Hamara
Affiliation:
University of Arizona, Tucson, Arizona
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Indices of normal spaces with countable basis for equivariant mappings have been investigated by Bourgin [4; 6] and by Wu [11; 12] in the case where the transformation groups are of prime order p. One of us has extended the concept to the case where the transformation group is a cyclic group of order pt and discussed its applications to the Kakutani Theorem (see [10]). In this paper we will define the Jp-index of a normal space with countable basis in the case where the transformation group is a cyclic group of order n, where n is divisible by p. We will decide, by means of the spectral sequence technique of Borel [1; 2], the Jp-index of SO(n) where n is an odd integer divisible by p. The method used in this paper can be applied to find the Jp-index of a classical group G whose cohomology ring over Jp has a system of universally transgressive generators of odd degrees.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 22 , Issue 4 , 01 August 1970 , pp. 705 - 712
Copyright
Copyright © Canadian Mathematical Society 1970

References

1. Borel, A., Sur la cohomologie des espaces fibres principaux et des espaces homogènes de groupes de Lie compacts, Ann. of Math. (2) 57 (1953), 115–207.Google Scholar
2. Borel, A., Sur Vhomologie et la cohomologie des groupes de Lie compacts connexes, Amer. J. Math. 76 (1954), 273–342.Google Scholar
3. Borel, A. (with contributions by Bredon, G., Floyd, E. E., Montgomery, D., and Palais, R.), Seminar on transformation groups, Ann. of Math. Studies, No. 46 (Princeton Univ. Press, Princeton, N. J., 1960).Google Scholar
4. Bourgin, D. G., Some mapping theorems, Rend. Math, e Appl. (5) 15 (1957), 177–189.Google Scholar
5. Bourgin, D. G., Modern algebraic topology (Macmillan, New York, 1963).Google Scholar
5. Bourgin, D. G., Multiplicity of solutions in frame mappings, Illinois J. Math. 9 (1965), 169–177.Google Scholar
7. Bourgin, D. G., Multiplicity of solutions in frame mappings. II, Illinois J. Math. 10 (1966), 557–562.Google Scholar
8. Liao, S. D., A theorem on periodic transformations of homology spheres, Ann. of Math. (2) 56 (1952), 68–83.Google Scholar
9. Swan, R. G., A new method infixed point theory, Comment. Math. Helv. 84 (1960), 1–16.Google Scholar
10. Wakae, M., Some results on multiplicity of solutions in frame mappings, Math. Z. 98 (1967), 407–421.Google Scholar
11. Wu, Wen-Tsün, On the Φ(p)-classes of a topological space, Sci. Record (N.S.) 1 (1957), 377–380.Google Scholar
12. Wu, Wen-Tsün, On the dimension of a normal space with countable basis, Sci. Record (N.S.) 2 (1958), 65–69.Google Scholar