〈 Berger | Dillon 〉

Physicist here.. what does it mean to 'fiber' a curve?

Here it’s like a fiber bundle (which is like a vector bundle but for more general types of spaces) except there can be some “singularities” or points where some of the spaces are bad. That happens three times in this example - when circles break off / recombine or collapse.

i see .. i still am not sure what a Fiber bundle is with 100% confidence .. wanna ELi5 for good measure (no pun intended)?

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)

A fiber bundle is a space that you can describe this way locally: that means you can chop it into pieces so that each piece looks just like a bundle of wheat: a bunch of parallel spaces stacked right next to one another. The spaces you're stacking together are called the fibers

ah that makes a lot of sense .. thanks so much