The loop cohomology of a space with the polynomial cohomology algebra
Abstract
Given a simply connected space X with the cohomology H*(X; Z2) to be polynomial, we calculate the loop cohomology algebra H*( X; Z2) by means of the action of the Steenrod cohomology operation Sq1 on H*(X; Z2). As a consequence we obtain that H*( X; Z2) is the exterior algebra if and only if Sq1 is multiplicatively decomposable on H(X; Z2). The last statement in fact contains a converse of a theorem of A. Borel.
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