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?

linkedfor that, generally they'd refer to that asknotting. If there's more than one $S^1 \times S^1$, then people refer to linking. – Ryan Budney May 3 '13 at 5:03