I have a basic question which I am not able to figure out. If we do a Gluck twist on a nullhomologous 2-sphere in a 4-manifold, it is said that it does not change its intersection form. But as far as I understand the Gluck twist changes the framings and knotting of the link 
components which represent the second homology. So why doesn't the intersection form change?



Gluck twist on four-manifolds
Basically this is Lefschetz duality. Chopping out the neighbourhood of the 2-sphere gives a 4-manifold $X$ with boundary $Y = S^2 \times S^1$. You can think about the intersection form here and how this will change after the surgery.


The point of $S^2$ being null-homologous is that if you look at the long exact sequence on homology (say) of the pair $(X,Y)$ you will see that every element of $H\_2(X,Y)$ is represented by a unique element of $H\_2(X)$.


I think it's necessary that the $S^2$ be null-homologous, I would imagine that otherwise, a priori, the intersection form may change.


