Some properties of Hopf-type constructions
1995 ◽
Vol 117
(2)
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pp. 287-301
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If f: X × Y → Z is a map, then the classical Hopf construction associates to f a map hf: X * Y → ΣZ, where X * Y is the join of X and Y and ΣZ the suspension of Z. Since X * Y has the homotopy type of Σ(X Λ Y), the suspension of the smash product of X and Y, the homotopy class of hf can be regarded as an element Hf ↦ [Σ(X Λ Y), ΣZ]. Now elements of [Σ(X Λ Y), ] are in one to one correspondence with homotopy classes in the group [σ(X Λ Y), ΣZ] which are trivial on the suspension of the wedge Σ(X ≷ Y).
1972 ◽
Vol 24
(5)
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pp. 789-791
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1992 ◽
Vol 112
(2)
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pp. 281-285
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2018 ◽
Vol 17
(05)
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pp. 1850081
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1968 ◽
Vol 64
(1)
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pp. 11-14
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2010 ◽
Vol 12
(05)
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pp. 871-908