Fiber Bundle Topology

Base space × Fiber = Total space (locally) — but globally twisted

Möbius Band
Hopf Fibration S³→S²
Cylinder (trivial)

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Möbius Band: fiber bundle with base S¹ (circle) and fiber I (interval). One twist → non-orientable, non-trivial bundle. Two twists → cylinder (trivial). The holonomy around the base loop rotates the fiber by π per twist.