A rather obscure method of colonizing gas giants. The idea is that you have a massive plate or strip, thousands of miles long, upon which a colony is built. The colony floats in the upper atmosphere of a gas giant, held aloft by dynamic mass streams--large columns of gas electromagnetically propelled skyward. Atmosphere could be retained by a high wall of hydrogen gasbags, or possibly even a layer of specialized utility fog. (The latter would be prettier and allow solid objects to pass through.)
Appears in The Causal Angel and Orion's Arm, so I figured it had to originate from somewhere. It took a little while to track down the original paper, but it's out there:
(Thanks, archive.org. I <3 you.)
This is probably the finest method of gas giant colonization I have heard of due to the massive living space. The other method that comes to mind is colossal vacuum-based hybrid airships (two links) the size of cities, so large they make the Hindenburg look like a toy blimp.
Also useful for colonizing brown dwarfs.