Definition of Line Bundle
Definition. Line bundle
A line bundle over a space X is a map π: L → X such that each fiber Lx = π-1(x) is a one-dimensional vector space.
Locally, it looks like a product U × ℝ or U × ℂ.
The key point is local triviality: locally product-like, globally possibly twisted.
Example: the Möbius strip is a real line bundle over S1.
base angle t = 0.90
Each point of S1 has a line attached to it, but after going once around the circle, the line returns with a twist.
(m, n) = (0, 0)
e-nλ = 1.00
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Drag the mouse to turn your view. Walk with W/A/S/D or arrow keys. Left and right copies keep the same size, while forward copies shrink and backward copies grow by e-nλ.