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The Poincare Polynomial of a Symmetric Product

Published online by Cambridge University Press:  24 October 2008

I. G. Macdonald
I. G. Macdonald
Affiliation:
Exeter University
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Extract

Let X be a compact polyhedron, Xn the topological product of n factors equal to X. The symmetric group Sn operates on Xn by permuting the factors, and hence if G is any subgroup of Sn we have an orbit space Xn/G obtained by identifying each point of Xn with its images under G. In particular Xn/Sn is the nth symmetric product of X, and if G is a cyclic subgroup of order n then Xn/G is the nth cyclic product of X.

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 58 , Issue 4 , October 1962 , pp. 563 - 568
Copyright
Copyright © Cambridge Philosophical Society 1962

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References

REFERENCES

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