Two years ago, Joel Friedman submitted a paper purporting to prove the Hanna Neumann Conjecture, which eventually turned out to contain a fatal bug and was withdrawn. Quite recently, Friedman repeated his attempt at proof with paper "Sheaves on Graphs and a Proof of the Hanna Neumann Conjecture": http://arxiv.org/abs/1105.0129 . Has this attempt been verified by anyone or is still under review?
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I don't think that this latest round has been independently verified.
Igor Mineyev has also announced a solution. See http://www.math.uiuc.edu/~mineyev/math/