and
rational homotopy theory (equivariant, stable, parametrized, equivariant & stable, parametrized & stable)
Examples of Sullivan models in rational homotopy theory:
Let be a finite dimensional simply connected compact Lie group, with Lie algebra denoted
Then the Sullivan minimal model of the classifying space is the graded algebra
of invariant polynomials on , equipped with vanishing differential:
That the rational cohomology of is given by
is due to Chern 50, (11), Bott 73, p. 239 (5 of 15).
(Here is the ground field of characteristic zero).
That the rational cohomology algebra of , with trivial differential, is the minimal Sullivan model for is discussed for instance in (Félix-Oprea-Tanré 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 August 27, 2020 at 15:15:07. See the history of this page for a list of all contributions to it.