There's been a bit of flip-flopping from various AMD sources and reports about whether their Mantle API will come to Linux in the near-term, which is AMD's high-performance graphics API designed to complement OpenGL and Direct3D for the gaming space by offering faster frame-rates. Mantle for now remains Windows-only and bound to just the Catalyst driver with the more recent "GCN" graphics cards.
Recently there's been mentions of AMD Mantle and Linux, but nothing too concrete. Richard Huddy, AMD's Gaming Scientist and a recent hire at the company, is now indicating that in fact Mantle will come to Linux.
Confirmation of the report can be found at PCWorld.com. "The company has received requests from developers to port Mantle to Linux, Huddy said. AMD over time will dedicate resources to the task, Huddy said. AMD hasn’t provided a time frame for when Mantle-based games for Linux will become available."
The same AMD employee was cited in the same article that Mantle is also an "open-source API" but hasn't been opened yet... "Huddy said that Mantle is an open-source API. But the Mantle tools have largely been shared with game makers, and the company has not said when they will be opened up to the wider development community."
So at the end of the day it's still not too much information over what we've known for a while that AMD will quite possibly bring Mantle to Linux in the end, but it could be a long wait, and when it comes will quite potentially be limited to just the Catalyst driver unless they start investing more into their open-source driver stack -- even with their more open driver strategy currently being explored. When and how open Mantle will be also remains to be seen, but hopefully OpenGL 5.0 will be able to cause greater competition and force AMD to be more open with Mantle.