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Symmetric products of the circle

Published online by Cambridge University Press:  24 October 2008

H. R. Morton
H. R. Morton
Affiliation:
University of Warwick, Coventry
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Extract

The nth symmetric product of a topological space, X, is defined to be the quotient of the Cartesian product Xn by the action of the symmetric group which permutes the factors. Even if X is a manifold, this product is, in general, not a manifold. The purpose of this note is to determine these products when X is the circle, S1, and to show that they are manifolds with boundary.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 63 , Issue 2 , April 1967 , pp. 349 - 352
Copyright
Copyright © Cambridge Philosophical Society 1967

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