Special Relativity only applies if the space between A and B is relativity flat. As long as space is flat in the vicinity, then the predictions of Special Relativity hold true. It doesn't matter if you made some weird topological wormhole that provides a shorter path. If Special Relativity has shown you how to, for instance, make a closed causal curve in the flat part of the space, using the events that occur in the flat part of the space, then SR will be correct in that prediction. The fact that there are non-flat parts of space elsewhere that were used to facilitate the aforementioned events in the flat part, is irrelevant to SR.
If, on the other hand, you are talking about cosmological wormholes that might let you travel some place that is far, far away--e.g., outside our Hubble sphere--then Special Relativity might not apply. For instance if the reason we can have a wormhole is because
space ever-so-slowly curves back onto itself, and there ends up being a short little bridge between two pieces of the universe that turn out to be very close to each other in the space that encloses our 3D space, but far away when measured as an ant crawls within our space, then Special Relativity won't be of use because the space between A and B is not flat. But in that case, GR lets you violate causality with such wormholes, even if you can no longer analyze the issue with SR:
You can write to me at doug at alum.mit.edu, but I can't provide much deep insight to GR, as my knowledge of it isn't much more than that of a knowledgeable layperson. I only really understand SR and when it can be applied.
If, on the other hand, you are talking about cosmological wormholes that might let you travel some place that is far, far away--e.g., outside our Hubble sphere--then Special Relativity might not apply. For instance if the reason we can have a wormhole is because space ever-so-slowly curves back onto itself, and there ends up being a short little bridge between two pieces of the universe that turn out to be very close to each other in the space that encloses our 3D space, but far away when measured as an ant crawls within our space, then Special Relativity won't be of use because the space between A and B is not flat. But in that case, GR lets you violate causality with such wormholes, even if you can no longer analyze the issue with SR:
http://en.wikipedia.org/wiki/Worm_holes#Time_travel
You can write to me at doug at alum.mit.edu, but I can't provide much deep insight to GR, as my knowledge of it isn't much more than that of a knowledgeable layperson. I only really understand SR and when it can be applied.