I'm simultaneously learning some group theory and differential geometry in different contexts and I find myself wondering....
We utilize an affine connection in general relativity (specifically a torsionless levi-cevita type usually), but can imagine using a general affine connection as well. No group theory is ever mentioned.
On the other side of the coin, I'm learning that the double cover of the Poincare group is the special affine group, which has innumerable physical applications. What's the deal, the two are clearly related in some way, but neither class mentions anything suggesting the link.