#fiber bundle

[grrlmusic]

Solma - Fiber Bundle

[knotoriginal]

arroyo fringe effects art yarn bundle

[allofthemath]

This is a depiction of a fiber bundle, a mathematical object I have been trying to figure out for about a week. From what I understand, you have a total space, E, and that maps to the base space B. Above, everything you see is E, and the flat part is B. The map takes you from wherever you are (on the flat part or along any of the fibers) to the dot on the flat part (base space) from which the fiber you're on emerges.

In the most basic case, E=BxF, which is to say that the total space is just all possible combinations of a base dot and then where along the fiber emerging from the dot you are. But the interesting part is when E is more complicated than that, but in small areas acts just like that set of possible combinations.

Anyone want to help explain more? Give examples?

[ernestyalumni]

Would you like some quick and dirty tricks with linear algebra? In the linked video, I give some quick and dirty tips when dealing with the differential. You remember the differential from multilinear calculus. You saw it as the Jacobian. You needed the determinant of the Jacobian for calculating change of variables in multivariable integrals. a) throw out what you learned with multivariable integration; check out integrating p-forms and all the pain of change of variables go away. b) The big boy way to think about the differential is that it's a linear, continuous differentiable transformation between manifolds. Now I always forget, when the differential is maximal rank, when it's injective and surjective and I draw a few diagrams that'll help out. Be sure, if you find this video useful, to like it, subscribe, and to check back in on any of your favorite social media platforms! And do you want to help fund science? Check out my indiegogo page! Facebook : ernestyalumni gmail : ernestyalumni linkedin : ernestyalumni tumblr : ernestyalumni twitter : ernestyalumni weibo 微博 : ernestyalumni youku : ernestyalumni youtube : ernestyalumni indiegogo : ernestyalumni

[ernestyalumni]

Visualization of the Hopf Fibration - Niles Johnson's presentation at an introductory level of the Hopf Fibration is very enjoyable to watch what the Hopf fibration, a fiber bundle or locally trivial bundle, means and what it looks like (visualize!).

[microscopic-masterpiece-blog]

1991: Polyurethane elastic fiber bundle (25x), Polarized Light. / Marc Van Hove, Centexbel, Belgium. Courtesy of Nikon Small World.