A cubic surface, fibered by elliptic curves.pic.twitter.com/fbKhRYO9ef
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By telling me you've stacked a bunch of wheat together so the cross section looks like a disk, I could develop a sort of picture for what you are talking about (the bundle of wheat, a 3d thing) in terms of simpler data: a single fiber of wheat (1d) and the cross section (2d)
so the fiber essentially tells you how the cross section changes increase some parameter?
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oh shit is this where the connection comes in? please say yes
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This is where connections come in! All the fibers in our bundle look the same, and so we might want a way to rigorously encode this, to connect different fibers. Let’s think about vector bundles, so you have a vector space tacked on to your base manifold at every point.
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