I have two questions that seem to be related.


I wonder if there is a user-friendly algorithm (starting from ribbon/slice presentation of knots/disks) for the construction of double (in general $p$-fold) coverings of $B^4$ along ribbon/slice disks.


Using the handle decomposition of ribbon/slice disks can we control the handle decomposition of double (in general $p$-fold) coverings of $B^4$ along these disks?



Double ($p$-fold) coverings of $B^4$ along ribbon/slice disks
I would like to popularize the lecture notes of Brendan Owens about the double branched cover of knots in $S^3$ and of ribbon/slice disks in $B^4$.


He both discussed constructions and obstructions. Also, it includes the classical references listed by Professor Ruberman.



> 
> Owens, Brendan. "Knots and 4-manifolds." Winter Braids Lecture Notes 6 (2019): 1-26.
> 
> 
> 


It is avaliable online [here](https://wbln.centre-mersenne.org/item/?id=WBLN_2019__6__A2_0).


