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The projective plane of an $$H$$-pairing. (English) Zbl 0757.55011
Summary: The projective plane of an $$H$$-space has played an important role in the theory of $$H$$-spaces. In particular, if the cohomology of a given $$H$$- space is primitively generated, the cohomology of its projective plane has a simple structure. In this paper we discuss the projective plane of an $$H$$-pairing which is a generalized concept of an $$H$$-space. This extension gives us a method to construct a projective plain-like space out of an $$H$$-space. This space turns out to be useful even if the cohomology of the $$H$$-space is not primitively generated. As an application we prove some facts on the action of the squaring operations on the cohomology of a finite $$H$$-space.

MSC:
 55P45 $$H$$-spaces and duals 55S10 Steenrod algebra
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References:
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