The Positive Mass Conjecture for Non-spin Manifolds
  We extend Witten's spinor proof of the positive mass theorem to large classes of complete asymptotically flat non-spin manifolds, including all manifolds of dimension less than or equal to 11 and all manifolds of dimension less than 26 which admit a codimension 3 immersion in Euclidean space. 
Anda Degeratu and Mark Stern