Every locally compact group is the outer automorphism group of a II1 factor

We prove that every locally compact second countable group G arises as the outer automorphism group Out M of a II1 factor, which was so far only known for totally disconnected groups, compact groups, and a few isolated examples. We obtain this result by proving that every locally compact second countable group is a centralizer group, a class of Polish groups that arise naturally in ergodic theory and that may all be realized as Out M.