I am now facing a problem with "surface link" in four dimension. I have heard that three 2-torus can be linked in four dimension. And I have created a movie by cutting four dimensional space with series of parallel three dimension spaces. However, I still do not know how to visualize the link. In other words, which phenomena in the movie can tell me these three 2-torus are really linked?
Besides, is there general "knot theory of surface" in four dimension space? Is there topological invariant (such as Jones polynomial) to characterize "knot" in four dimension?