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On cyclic maps

Published online by Cambridge University Press:  24 October 2008

V. P. Snaith
V. P. Snaith
Affiliation:
Emmanuel College, Cambridge
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Extract

Throughout X will denote a connected, finite C.W. complex.

Let G be a subgroup of ∑n, the symmetric group, which acts transitively on the Cartesian product, Xn, of the space X. A map f:Xn→X is G-symmetric if it commutes with the action of G. If x0εX is a base point let i:X→Xn denote the inclusion, i(x) = (x,x0, …,x0). In ((6); (7); (11)–(13)) the following problem is posed: if X is an orientable topological n-manifold, what is the set of integers which may be obtained as the degree of(f.i) where f is a G-symmetric map? The degree of(f.i) is called the James number of f. If G = ∑n(G = Zn) a G-symmetric map will be called a symmetric map (a cyclic map). If X = Sn, the n-sphere, this problem has been studied in ((6)–(8), (11)–(13))

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 71 , Issue 3 , May 1972 , pp. 449 - 456
Copyright
Copyright © Cambridge Philosophical Society 1972

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References

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