IMHO cnts will never be made into a fiber long enough without atomic defects. (in this case: defects = reduced strength) It would be a bit like being victorious over entropy.
In the end it is probably cheaper to only get up into orbit what really needs to come from earth (i.e. life and data) and get anything else directly from space (asteroids and so on) without fighting gravity.
The wiki page of space elevators seems to link to some more serious articles (e.g.: References 2, 4, 6 8, 29, 31...) Finding many hard science articles about space elevators is probably quite difficult as the fundamentals (building material, location and exact concept) are not available (yet).
You can start reading plenty of articles on nano tubes and nano mechanics but this might lead you astray.