Vol. 87, No. 2, 1980

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Mod p decompositions of H-spaces; another approach

John Henry McCleary

Vol. 87 (1980), No. 2, 373–388

Let M and Mbe unstable modules over the mod p Steenrod algebra such that there are spaces Y and Y with H(Y ;Zp) = U(M) and H(Y ;Zp) = U(M). Here U( ) is the free-associative-graded-commutative-unstable algebra functor introduced by Steenrod. Suppose g : M′→ M is a morphism of unstable modules. We develop an obstruction theory which decides when g can be realized by a map G : Y (p) Y (p), that is, g = H(G,Zp)|M. We then apply this obstruction theory to obtain p-equivalences of certain H-spaces with products of spheres and sphere bundles over spheres which are determined by the cohomology structure of the H-space.

Mathematical Subject Classification 2000
Primary: 55P45
Received: 14 December 1978
Published: 1 April 1980
John Henry McCleary