Representing Homology Automorphisms of Nonorientable Surfaces

John D. McCarthy
Department of Mathematics
Michigan State University
E. Lansing, MI 48824-1027

Ulrich Pinkall
Technische Universitat Berlin
Sekr. MA 3-2
Str. des 17. Juni 136
10623 Berlin, Germany

Let F_p be a closed, connected, nonorientable surface of genus p. Let H₁(F_p,Z) be the first homology group of F_p with integer coefficients. In this paper, we prove that each automorphism of H₁(F_p,Z) which preserves the Z₂-valued intersection pairing is induced by a diffeomorphism of F_p.