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WebTo answer (1), the idea would be to try and construct a trivialization "by hand". For principal bundles, that means a section. Think of a circle as an interval with the endpoints identified. Constructing the section on an interval is easy (path-lifting property of a bundle) but then you have to check that you can ensure the endpoints meet up. In mathematics, a circle bundle is a fiber bundle where the fiber is the circle $${\displaystyle S^{1}}$$. Oriented circle bundles are also known as principal U(1)-bundles. In physics, circle bundles are the natural geometric setting for electromagnetism. A circle bundle is a special case of a sphere … See more Circle bundles over surfaces are an important example of 3-manifolds. A more general class of 3-manifolds is Seifert fiber spaces, which may be viewed as a kind of "singular" circle bundle, or as a circle bundle over a two … See more The isomorphism classes of principal $${\displaystyle U(1)}$$-bundles over a manifold M are in one-to-one correspondence … See more The Maxwell equations correspond to an electromagnetic field represented by a 2-form F, with $${\displaystyle \pi ^{\!*}F}$$ being cohomologous to zero, i.e. exact. In particular, there always exists a 1-form A, the electromagnetic four-potential, (equivalently, the See more • Wang sequence See more WebTip! - the calculator above can be used to approximate the outside diameter of a bundle of pipes by inserting the small pipe diameter and do an iterative changing of the outside pipe diameter until the number of pipes … green burnishing pads