Three remarks on symmetric products and symmetric maps

V. P. Snaith; J. J. Ucci

doi:10.2140/pjm.1973.45.369

Three remarks on symmetric products and symmetric maps

V. P. Snaith, J. J. Ucci

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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^mSⁿ. The final remark provides a group-theoretic construction of G-maps f: (S_n)_m → Sⁿ where G ⊂ S(m) acts on (Sⁿ)^m by permutation of its factors.

Original language	English (US)
Pages (from-to)	369-377
Number of pages	9
Journal	Pacific Journal of Mathematics
Volume	45
Issue number	1
DOIs	https://doi.org/10.2140/pjm.1973.45.369
State	Published - Mar 1973

ASJC Scopus subject areas

General Mathematics

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10.2140/pjm.1973.45.369

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AB - 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 nth suspension space. Remark two generalizes a well-known adjunction formula for SP2Sn due to Steenrod to a filtration of length m of SPmSn. 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.

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Three remarks on symmetric products and symmetric maps

Abstract

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