@BalarkaSen the height function on the circle is not submersive at the interval boundary, unless I'm misunderstanding your example
@BalarkaSen I initially wanted to avoid going through the proof again to see this (the authors of the paper certainly seem to imply it's rather straightforward), but in any case this does sound convincing
Given a compact Riemann surface $S$, does a homotopy class of map $f:S\to\Bbb CP^1$ uniquely determine the complex line bundle on $S$ up to isomorphism?
