mathwonk's latest activity

Just found a really good lecture on tensors. It starts with the absolute basics and goes all the way up to universal mapping:

nice spoiler. took me a while to grasp, the key for me being that the map psi is itself bilinear, indeed it is the universal bilinear map.

I think this will always occur when people can bestow a benefit at no cost to themselves. The DeviantArt site had an award called a...

absurd "coincidence": when I "solved " it (completely wrong) by confusing tangent with cosine, I got sqrt(11/4); and the actual answer...

I want to describe some geometry that seems to connect to lavinia's vector field discussion, which I have yet to grasp. Lavinia has...

RE: post #33: yes, I tried to say something like this in post #10.

In terms of the sequence, SO(2)->SO(3)->S^2, since SO(2) is closed in SO(3) ,this sequence describes a fiber bundle whose fibers are...

This is getting clearer, if slowly. We know every (non trivial) rotation about a given axis, belongs to a circle subgroup of rotations...

Building again on lavinia's posts, we know SO(3) is homeomorphic to RP^3, the real projective 3-space, which is a solid ball with...

@Matterwave The first description in Post #9 of the tangent circle bundle of the 2 sphere as a circlular stack of of projective planes...

The Tangent Circle Bundle of the 2-Sphere Here is a way to “visualize” the tangent circle bundle of the 2-sphere that connects to a lot...

Briefly, starting from the Hopf fibration, in each fiber just identify each point on the circle with its opposite point. Since...

Yeah this makes sense! Let me try to write this out. You are describing thinking of a ##SO(3)## matrix like: $$ O=\begin{pmatrix}\vert &...

disclosure: I have not studied bundle theory and euler classes, and was not aware that circle bundles are often assumed to have a given...

To expand @wroblel's point in post #3: The action of SO(3) on the 2 sphere can be extended to an action on its tangent circle bundle...