## Homology, Homotopy and Applications

### The set of rational homotopy types with given cohomology algebra

#### Abstract

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.

#### Article information

Source
Homology Homotopy Appl., Volume 5, Number 1 (2003), 423-436.

Dates
First available in Project Euclid: 13 February 2006

https://projecteuclid.org/euclid.hha/1139839941

Mathematical Reviews number (MathSciNet)
MR2072343

Zentralblatt MATH identifier
1067.55003

Subjects
Primary: 55P62: Rational homotopy theory

#### Citation

Shiga, Hiroo; Yamaguchi, Toshihiro. The set of rational homotopy types with given cohomology algebra. Homology Homotopy Appl. 5 (2003), no. 1, 423--436. https://projecteuclid.org/euclid.hha/1139839941