Note on the Whitehead Product

1953 ◽  
Vol 58 (3) ◽  
pp. 429 ◽  
Author(s):  
P. J. Hilton ◽  
J. H. C. Whitehead
Keyword(s):  
Whitehead Product

A Note on the Homotopy-Commutativity of Suspensions

1967 ◽  
Vol 10 (5) ◽  
pp. 665-668
Author(s):  
C.S. Hoo
Keyword(s):  
Whitehead Product ◽  
Base Points

Let A and X be spaces. Then as is wellknown, [∑A, X] is a group where ∑ denotes the suspension. We wish to find conditions on A which will imply that this group is abelian for all spaces X, that is, ∑A is homotopy-commutative. This is equivalent to saying that conii A≤ 1 (see [2] for definition). Our results contain relations between conil A and the generalised Whitehead product of [1]. We work in the category of complexes with base points.

scholarly journals Remarks on the realizability of Whitehead product

1960 ◽  
Vol 12 (1) ◽  
pp. 130-138 ◽  
Author(s):  
Kôichi Iwata ◽  
Hiroshi Miyazaki
Keyword(s):  
Whitehead Product

A certain triple Whitehead product

1954 ◽  
Vol 50 (2) ◽  
pp. 189-197 ◽  
Author(s):  
P. J. Hilton
Keyword(s):  
Jacobi Identity ◽  
Whitehead Product ◽  
Image Position

The triple Whitehead product we consider in this note is [[ɩn, ɩn], ɩn] ∈ π3n−2(Sn), where ɩn generates πn(Sn). It follows from the Jacobi identity for Whitehead productsα ∈ πp(X), β ∈ πq(X), γ ∈ πr(X), that 3[[ɩn, ɩn], ɩn] = 0. Now, if n is odd, 2[ɩn, ɩn] = 0, so that 2[[ɩn, ɩn], ɩn] = 0, whence

scholarly journals On distinguishing spaces not homotopy-equivalent

1994 ◽  
Vol 49 (1) ◽  
pp. 117-119
Author(s):  
M.H. Eggar
Keyword(s):  
Cohomology Ring ◽  
Product Structure ◽  
Homotopy Equivalent ◽  
Topological Spaces ◽  
Homotopy Groups ◽  
Whitehead Product ◽  
Homology Groups

A non-pathological example is given of two topological spaces which have isomorphic homotopy groups, homology groups and cohomology ring and which cannot be distinguished from each other by the Whitehead product structure. A family of examples can be constructed likewise.

scholarly journals The generalized Whitehead product

1962 ◽  
Vol 12 (1) ◽  
pp. 7-23 ◽  
Author(s):  
Martin Arkowitz
Keyword(s):  
Whitehead Product

scholarly journals A Whitehead product for Track Groups II

1989 ◽  
Vol 33 ◽  
pp. 205-212 ◽  
Author(s):  
K. A. Hardie ◽  
A. V. Jansen
Keyword(s):  
Whitehead Product
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