Obstruction theory in fiber spaces

Embeddings and immersions of manifolds in Euclidean space

“…An element y ® a EA(B) acts on x E H*(X: Z2)byy®a-x= g*(y) U a(x) (recall g: X -► B) and is called a twisted primary cohomology operation. Relations in A(B) give rise to twisted secondary operations; they are studied in [17].…”

“…This is a formal procedure, the details of which may be found in [17] in case p is simple and in [18] in the nonsimple case. The idea behind this transformation is the following.…”

Spaces of sections of Eilenberg-Mac Lane fibrations

“…We shall be particularly interested in the K(π, l)-sectioned spaces [10] that arise in the following way. Suppose that G is a system of local coefficients in the Eilenberg-Mac Lane space K(π, 1) given by a homomorphism φ: TΓ^A^TΓ, 1)) = m -» Aut(G 0 ) of π into the automorphism group of a typical group G o of G. For any integer n > 0, G may be realized, see ( [5], Ch.…”

“…Suppose that G is a system of local coefficients in the Eilenberg-Mac Lane space K(π, 1) given by a homomorphism φ: TΓ^A^TΓ, 1)) = m -» Aut(G 0 ) of π into the automorphism group of a typical group G o of G. For any integer n > 0, G may be realized, see ( [5], Ch. Ill) or ( [10], p. 7), as the system of local coefficients defined by the π-dimensional homotopy groups of the fibres of a sectioned fibration n;φ)ϊtK(ττ,l) k over K{ π, 1). This fibration, which we shall denote by κ (G, n) for any map u: X -> K(G 0 , n φ) with u x = ku.…”

“…This fibration, which we shall denote by κ (G, n) for any map u: X -> K(G 0 , n φ) with u x = ku. Via pull-back of the path-space fibration in the category of K(tt, l)-sectioned spaces [10],…”