Circle Bundle

A circle bundle pi:E->M is a fiber bundle whose fibers pi^(-1)(x) are circles. It may also have the structure of a principal bundle if there is an action of SO(2) that preserves the fibers, and is locally trivial. That is, if every point has a trivialization U×S^1 such that the action of SO(2) on S^1 is the usual one.

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This entry contributed by Todd Rowland

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Rowland, Todd. "Circle Bundle." From MathWorld--A Wolfram Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/CircleBundle.html

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