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The Poincare Polynomial of a Symmetric Product

  • I. G. Macdonald (a1)

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.

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(1)Grothendieck, A., Sur quelques points d'algébre homologique. Tôhoku Math. J. 9 (1957), 119221.
(2)Hilton, P. J., and Wylie, S., Homology theory (Cambridge University Press, 1961).
(3)Littlewood, D. E., A university algebra (Heinemann; London, 1950).
(4)Richardson, M., On the homology characters of symmetric products. Duke Math. J. 1 (1935), 5069;
correction, On the homology characters of symmetric products. Duke Math. J.. 3 (1937), 382.
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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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