nLab Sullivan model of complex projective space

Statement

The Sullivan model of complex projective space $\mathbb{C}P^n$ is

(1)$$\mathbb{Q} [ f_2, h_{2n+1} ] \big/ \left( \begin{aligned} d\,f_2 & = 0 \\ d\,h_{2n+1} & = (f_2)^{n+1} \end{aligned} \right)$$

(e.g. Félix-Halperin-Thomas 00, p. 203, Menichi 13, 5.3)

Related concepts

Examples of Sullivan models in rational homotopy theory:

• Sullivan model of an n-sphere

• Sullivan model of a spherical fibration

• Sullivan model of complex projective space

• Sullivan model of a classifying space

• Sullivan model of mapping space

• Sullivan model of free loop space

• Sullivan model of a suspension

• Sullivan model of a finite G-quotient

References

• Alan J. Deschner, Exp. 3.5 (b) in: Sullivan’s theory of minimal models, MSc thesis, Univ. British Columbia (1976) [doi:10.14288/1.0080132, pdf]

• Yves Félix, Stephen Halperin, Jean-Claude Thomas, Rational Homotopy Theory, Graduate Texts in Mathematics, 205, Springer-Verlag, 2000 (doi:10.1007/978-1-4613-0105-9)

• Luc Menichi, Rational homotopy – Sullivan models, IRMA Lect. Math. Theor. Phys., EMS (arXiv:1308.6685)