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, 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.

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, 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.