منابع مشابه
On Generalized Whitehead Products
We define a symmetric monodical pairing G ◦ H among simply connected co-H spaces G and H with the property that S(G◦H) is equivalent to the smash product G∧H as co-H spaces. We further generalize the Whitehead product map to a map G ◦ H → G ∨ H whose mapping cone is the cartesian product. Whitehead products have played an important role in unstable homotopy. They were originally introduced [Whi...
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It is proved that if E, F are infinite dimensional strictly convex Banach spaces totally incomparable in a restricted sense, then the Cartesian product E × F with the sum or sup norm does not admit a forward shift. As a corollary it is deduced that there are no backward or forward shifts on the Cartesian product `p1 × `p2 , 1 < p1 6= p2 < ∞, with the supremum norm thus settling a problem left o...
متن کاملWhitehead Products in Function Spaces: Quillen Model Formulae
We study Whitehead products in the rational homotopy groups of a general component of a function space. For the component of any based map f : X → Y , in either the based or free function space, our main results express the Whitehead product directly in terms of the Quillen minimal model of f . These results follow from a purely algebraic development in the setting of chain complexes of derivat...
متن کاملDeformations of Whitehead Products, Symplectomorphism Groups, and Gromov–Witten Invariants
homotopy groups π∗(Xλ)⊗Q for a family of topological spaces, once we know enough about their additive structure. This allows us to interpret the condition of realizing as an Ak map a multiple of a map f : S1 −→ G between two topological groups in terms of the existence of a rational Whitehead product of order k. Our main example will be when the Xλ are classifying spaces of symplectomorphism gr...
متن کاملOn Whitehead Precovers
It is proved undecidable in ZFC + GCH whether every Z-module has a {Z}-precover. Let F be a class of R-modules of the form C = {A : Ext(A,C) = 0 for all C ∈ C} for some class C. The first author and Jan Trlifaj proved [7] that a sufficient condition for every module M to have an F -precover is that there is a module B such that F = {B} (= {A : Ext(B,A) = 0}). In [8], generalizing a method used ...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2011
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-2011-05392-4