Homeomorphisms and the homology of non-orientable surfaces
  We show that, for a closed non-orientable surface $F$, an automorphism of $H_1(F,\Z)$ is induced by a homeomorphism of $F$ if and only if it preserves the (mod 2) intersection pairing. We shall also prove the corresponding result for punctured surfaces. 
Siddhartha Gadgil and Dishant Pancholi