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Some non-embedding theorems. (English) Zbl 0715.55001
Following the ideas of J. W. Alexander [Trans. Am. Math. Soc. 28, 301-329 (1926; JFM 52.0569.01)], F. P. Peterson [Bol. Soc. Math. Mex., II. Ser. 2, 9-15 (1957; Zbl 0080.382)] related the problem of embedding a finite CW-complex X in a sphere \(S^ N\) for N sufficiently large to the primary cohomology operations of X and their dual cohomology operations in \(S^ N-X\). He later used secondary cohomology operations [Ill. J. Math. 4, 397-404 (1960; Zbl 0093.369)] for deciding non-embeddability of finite complexes which are in some sense p-analogues of projective spaces. We extend this technique to higher operations and obtain some non-embedding theorems using some known secondary and tertiary operations.
55M05 Duality in algebraic topology
55S20 Secondary and higher cohomology operations in algebraic topology