Mod-2 Equivalence of the K-theoretic Euler and Signature Classes
  This note proves that, as K-theory elements, the symbol classes of the de Rham operator and the signature operator on a closed manifold of even dimension are congruent mod 2. An equivariant generalization is given pertaining to the equivariant Euler characteristic and the multi-signature. 
James F. Davis, Pisheng Ding