Grassmannnian is defined to be $U(n)/(U(k)\times U(n-k))=U(n) /H$, say. I have to show that the quotient map $q$ gives a fiber bundle. So, I have to get a map $\phi : U(n) \rightarrow Gr(k, \Bbb C)\times H $. So it will be $A \mapsto (AH, h) $ where $h$ is a member of $H$. Now the question is what that $h$ should be. Please help.
2026-03-25 15:41:03.1774453263
Grassmannian as a fiber bundle over $U(n)$.
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