A cubic surface, fibered by elliptic curves.pic.twitter.com/fbKhRYO9ef
-
But keep in mind that the surface shown above is not *exactly* a fiber bundle - iiuc it’s part of a more general concept called a fibration - w a fiber bundle all the fibers look the same...
oh i see .. so the fibre bundle is like "continuous" but in a more general sense?
-
-
you mean "locally" look the same?
-
“look the same” as in homeomorphic - topologically equivalent. (Homeomorphism = continuous bijection w continuous inverse). Fibrations are even more general than fiber bundles, but tbh I don’t know enough algebraic geometry to describe exactly what’s going on here
End of conversation
New conversation -
-
-
Yeah - I think about a fiber bundle with fiber F and base B kind of as a 'continuous family of copies of F parameterized by B'. This is why vector bundles are everywhere: to talk about a vector field on a manifold, you need a vector space at each point of the manifold first!
- 1 more reply
New conversation -
-
-
The wikipedia article on fiber bundles is really good https://en.m.wikipedia.org/wiki/Fiber_bundle?wprov=sfti1 …
Thanks. Twitter will use this to make your timeline better. UndoUndo
-
Loading seems to be taking a while.
Twitter may be over capacity or experiencing a momentary hiccup. Try again or visit Twitter Status for more information.