Three remarks on symmetric products and symmetric maps

Victor Snaith and John James Ucci

Vol. 45 (1973), No. 1, 369–377

DOI: 10.2140/pjm.1973.45.369

Abstract

The first remark establishes that the homotopy type of a certain space related to the m-fold symmetric product SP^mSⁿ 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 SP^m_lSⁿ. 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