Note on some Whitehead products

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...

Note on Cup-products

Whitehead 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...

Note on Some Oscillation Criteria1

then (1) must be oscillatory. Various refinements as well as variations of the criterion (3) were obtained by Hartman in [l]. The present note will be devoted to the derivation of two further criteria, given in (*) and (**) below, involving the function G(t) of (3). Let E(M, T) denote the set of points t of the half-line T^t < oo for which the function G(t) of (3) satisfies the inequality G(t) ...

Note on Some Gap Theorems