The Cohomology Algebra of Certain Loop Spaces
نویسنده
چکیده
The purpose of this paper1 is to determine the cohomology algebra of a loop space over a topological space whose cohomology algebra is a truncated polynomial algebra generated by an element of even degree. As special cases we obtain the well-known results when the base space has as cohomology algebra an exterior algebra (the base space an even dimensional sphere) or a polynomial algebra (the base space infinite dimensional complex projective space; compare also Theorem 2 in [l]). In particular, the result is applicable to loop spaces over complex and quaternionic projective w-spaces and the Cayley plane. Throughout, A will denote a commutative ring with unit and Aalgebra will mean an associative ^4-algebra with unit.
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