Some call them convertible top frames, but there is a lot more to them than that.
The section over the doors holding the foremost rail, fold in like scissors, bringing the header rail and the front rail back flush with the B-posts. The top is then tied back in a roll.
Finally, the large chrome supports on the outside, called landau bars, fold in half to allow the rest of the top to fold back out of the way, leaving the car completely open.
These sticks were completely restored, to the point of laminating new tack bars out of ash strips.