and
rational homotopy theory (equivariant, stable, parametrized, equivariant & stable, parametrized & stable)
Examples of Sullivan models in rational homotopy theory:
Let $G$ be a finite dimensional simply connected compact Lie group, with Lie algebra denoted $\mathfrak{g}$
Then the Sullivan minimal model of the classifying space $B G$ is the graded algebra
of invariant polynomials on $\mathfrak{g}$, equipped with vanishing differential:
That the rational cohomology of $B G$ is given by $inv(\mathfrak{g})$
is due to Chern 1950 (11); Bott 1973, p. 239 (5 of 15).
(Here $k$ is the ground field of characteristic zero).
That the rational cohomology algebra of $B G$, with trivial differential, is the minimal Sullivan model for $B G$ is discussed for instance in Félix, Oprea & Tanré 20 08.
Examples of Sullivan models in rational homotopy theory:
Shiing-shen Chern, Differential geometry of fiber bundles, in: Proceedings of the International Congress of Mathematicians, Cambridge, Mass., (August-September 1950), vol. 2, pages 397-411, Amer. Math. Soc., Providence, R. I. (1952) (pdf, full proceedings vol 2 pdf)
Raoul Bott, On the Chern-Weil homomorphism and the continuous cohomology of Lie-groups, Advances in Mathematics Volume 11, Issue 3, December 1973, Pages 289-303 (doi:10.1016/0001-8708(73)90012-1)
Yves Félix, John Oprea, Daniel Tanré, Algebraic models in geometry, Oxford University Press 2008 (pdf, ISBN:9780199206520)
Last revised on November 26, 2023 at 15:05:53. See the history of this page for a list of all contributions to it.