Vol. 45, No. 1, 1973

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ISSN: 0030-8730
Three remarks on symmetric products and symmetric maps

Victor Snaith and John James Ucci

Vol. 45 (1973), No. 1, 369–377
Abstract

The first remark establishes that the homotopy type of a certain space related to the m-fold symmetric product SPmSn of the n-sphere is that of an n-th suspension space. Remark two generalizes a well-known adjunction formula for SP2Sn due to Steenrod to a filtration of length m of SPmlSn. The final remark provides a group-theoretic construction of G-maps f : (Sn)m Sn where G S(m) acts on (Sn)m by permutation of its factors.

Mathematical Subject Classification
Primary: 55A15
Milestones
Received: 7 October 1971
Published: 1 March 1973
Authors
Victor Snaith
University of Sheffield
United Kingdom
John James Ucci