The set of rational homotopy types with given cohomology algebra

Abstract

For a given commutative graded algebra A ⁄ , we study the set MA⁄ = frational homotopy type of X j H ⁄ (X;Q) » A ⁄ g. For example, we see that if A ⁄ is isomorphic to H ⁄ (S 3 _ S 5 _ S 16 ;Q), then MA⁄ corresponds bijectively to the orbit space P 3 (Q)=Q ⁄ ‘ f⁄g, where P 3 (Q) is the rational projective space of dimension 3 and the point f⁄g indicates the formal space.