Vol. 45, No. 1, 1973

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Three remarks on symmetric products and symmetric maps

Victor Snaith and John James Ucci

Vol. 45 (1973), No. 1, 369–377

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
Received: 7 October 1971
Published: 1 March 1973
Victor Snaith
University of Sheffield
United Kingdom
John James Ucci