Skip to main content
×
×
Home

The Poincare Polynomial of a Symmetric Product

  • I. G. Macdonald (a1)
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.

Copyright
References
Hide All
(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.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed