Homotopy groups of the Grassmannian:

![](attachments/Pasted%20image%2020210505015323.png)

The Grassmannian functor as a [moduli space](moduli%20space.md)

![](attachments/Pasted%20image%2020210511151415.png)

Here $\CC^n_S := \CC^n \cross S$ is the trivial bundle.

See also the [affine Grassmannian](affine%20Grassmannian.md).