A structure suggested by BuckminsterFuller in 1951, consisting of an artificial ring built in space above the earth's equator. This could be done to connect the a bunch of SpaceElevators.
Not the same as RingWorld, which is a ring surrounding a star and is thus much larger.
This would obviously only be useful to connect SpaceElevators if it were rotating geosynchronously.... which goes without saying.
The structure would have minimum stress if attached to the SpaceElevators exactly at the altitude of geosynchronous satellites, roughly 1/3 of the way up. But perhaps other locations closer to or further from the earth might be possible.
What's the purpose of this structure?
Speculation: In theory, it takes less energy to ride the elevator up to the bridge, take the moving sidewalk over to the next elevator, then take the elevator down, than it does to fly directly in an airplane.
We already have hundreds of tons of communication satellites in geosynchronous orbit, and "we" put more up every year. If we keep putting more and more stuff into that narrow band, eventually it will become packed solid. Voila, the FullerRingBridge. No SpaceElevator necessary.
Although that would definitely be one of the more expensive ways of going about building one << it's iterative. We get satellites in the meantime.
And once you connected them together the resulting structure would become unstable, start oscillating, touch the atmosphere and disintegrate (if it hadn't through tidal stresses already). Maybe the space elevators would anchor it? Solid rings rotating around large gravitational fields don't work. -- TomAyerst (oops, that's already been covered in RingWorld)
This is pure speculation, but would it be more stable if you put it just above geosynch orbit, so there's a constant, slight (or not-so-slight) pull outwards by centripetal force? Or, for that matter, put the structure just below geosynch orbit and let gravity bow it inwards, creating the world's biggest suspension bridge using the space elevators as the pylons. Oh, and here's an interesting issue... how would the Moon's tidal forces affect such a structure?
Once you got the bridge done, you won't need anymore geosync satellites, you can just mount another antenna anywhere on the bridge! As long as their separation is wide enough for the ground station to resolve.
See also MegaStructures.