EU(1)

In a world of numbers and space, There's a group that holds a special place. U(n) is its name, so grand and true, Let me tell you what it can do. In BU(n), a space so fine, With a bundle EU(n), oh so divine, Hermitian bundles, they come to play, On paracompact X, they find their way. Pulling back EU(n), they find their match, By a map X to BU(n), they attach. Unique up to homotopy, you see, A mathematical marvel, oh so free. One construction, the Grassmannian's grace, Of n-planes in a Hilbert space's embrace. Infinite dimensions, a world untold, Where U(n)'s secrets begin to unfold. The other construction, a limit so grand, Of Grassmannians, hand in hand. N-planes in harmony, they unite, In a space that shines with pure delight. So let's explore the Unitary Group's might, In BU(n) and EU(n), shining so bright. Mathematics, a world of wonder and glee, Where U(n) dances with joyful glee. Random page: BYD C9