# The set of rational homotopy types with given cohomology algebra

## Hiroo Shiga and Toshihiro Yamaguchi

For a given commutative graded algebra $A^*$, we study the set ${\cal M}_{A^*} =$ $\{\mbox{rational homotopy type of }X \$ $| \ H^*(X;Q)\cong A^*\}$. For example, we see that if $A^*$ is isomorphic to $H^*(S^3\vee S^5\vee S^{16};Q)$, then ${\cal M}_{A^*}$ corresponds bijectively to the orbit space $P^3(Q)/Q^*\coprod \{*\}$, where $P^3(Q)$ is the rational projective space of dimension 3 and the point $\{*\}$ indicates the formal space.

Homology, Homotopy and Applications, Vol. 5(2003), No. 1, pp. 423-436

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