way to have a rope (buckytube or whatever) to space:
have a massive foundation, anchored in bedrock, attached to the bottom of the rope at the earth's equator. have a satellite attached to the top of the rope, somewhat further (or perhaps way further) than a geostationary orbit, orbiting obviously coplanar with the Earth's equator. having the satellite farther than a geostationary orbit will cause the rope to pull it along faster than it would otherwise orbit, thus keeping the rope up (including the weight of whatever is currently elevating up the rope) by centrifugal force, just like a sling.
the longer the rope is, the less massive the satellite has to be, though the rope itself may be very expensive so the most economical length could be minimal (Clarke belt), maximal (the length at which you need no satellite), or some specific length in between.