How can we calculate the 4-genus of a link L? The 4-genus is defined to be the minimal genus of orientable surface bounded by L in B^4. Is there any routine method to calculate that?


Especially, any good idea how to calculate the 4-genus of a 2-bridge link? Thanks.



4-genus of a 2-bridge link
You might get interesting lower bounds using [Rasmussen's s-invariant](http://arxiv.org/abs/math.GT/0402131), and his calculations of [the KR homology of 2-bridge links](http://arxiv.org/abs/math.GT/0508510). 


Or you might not. As Ryan says, there are various ways of bounding genus above and below, but unless you get lucky and two of them match, it can be hard to tell. The 4-genus of torus knots was an open problem for a scandalously long time (if my history is right, it was first proven in the 90's!).


