Apologies if this question is too naive, but it strikes at the heart of something that's been bothering me for a while. Under a diffeomorphism $\phi$ we can push forward an arbitrary tensor field $F$ ...
Basically an exotic sphere is topologically a sphere, but doesn't look like a one. Or more accurately: homeomorphic but not diffeomorphic to the standard Euclidean n-sphere The first exotic ...
My general premise is that I want to investigate the transformations between two distinct sets of vertices on n-dimensional manifolds and then find applications to theoretical physics by: ...