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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeMay 28th 2017

I wrote out some elementary details at basic complex line bundle on the 2-sphere.

• CommentRowNumber2.
• CommentAuthorTodd_Trimble
• CommentTimeMay 28th 2017

Isn’t it just the Hopf fibration $S^1 \to S^3 \to S^2$?

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeMay 28th 2017
• (edited May 28th 2017)

Sure, it’s the complex line bundle canonically associated to the complex Hopf fibration.

• CommentRowNumber4.
• CommentAuthorTodd_Trimble
• CommentTimeMay 28th 2017

I added in the description that this is the tautological line bundle of the complex projective line, which I think is probably the simplest description. Whether that belongs in the Idea section or not, I’ll let someone else decide.