Let $X$ be a 4-manifold and $\Sigma\_g\subset X$ be an embedded closed orientable genus = $g$ surface. Suppose $\Sigma\_g\subset X$ has a trivial closed normal bundle $N(\Sigma\_g) = \Sigma\_g\times D^2$. For a given self-diffeomorphism $h$ on $\Sigma\_g\times S^1$, we can define a new 4-manifold:


$$X(\Sigma\_g,h):=(X-\text{Int}N(\Sigma\_g))\cup\_{h}(\Sigma\_g\times D^2)$$


For example, in the case of $g=0$ this operation is called [Gluck construction](http://www.map.mpim-bonn.mpg.de/Gluck_construction), and in the case of $g=1$ it is well known as (generalized) logarithmic transformation. My question is:



> 
> Is there any research in the case of $g\geq2$?
> 
> 
> 


Thank you for your help.



Surgery along an embedded surface in a 4-manifold
For $g\geq 2$, this construction doesn't yield anything new. In this situation, any self-diffeomorphism of $\Sigma\_g \times S^1$ extends to a self-diffeomorphism of $\Sigma\_g \times D^2$, and hence your $X$ is unchanged.


