Homology, Homotopy and Applications

Volume 5 (2003)

Number 1

The set of rational homotopy types with given cohomology algebra

Pages: 423 – 436

DOI: http://dx.doi.org/10.4310/HHA.2003.v5.n1.a18

Authors

Hiroo Shiga (Department of Mathematical Sciences, College of Science, Ryukyu University, Okinawa, Japan)

Toshihiro Yamaguchi (Department of Mathematics Education, Kochi University, Kochi, Japan)

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.

Keywords

rational homotopy type, minimal algebra, k-intrinsically formal (k-I.F.)

2010 Mathematics Subject Classification

55P62

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