For a closed manifold $X$, suppose $b_2(X)=0$.
Question: For any complex line bundle $L\to X$, can we always find a flat connection, i.e. does there exist a connection $\nabla$, such that $\nabla^2=0$?
For a closed manifold $X$, suppose $b_2(X)=0$.
Question: For any complex line bundle $L\to X$, can we always find a flat connection, i.e. does there exist a connection $\nabla$, such that $\nabla^2=0$?