  Let $\Sigma$ be a surface with a symplectic form, let $\phi$ be a
symplectomorphism of $\Sigma$, and let $Y$ be the mapping torus of $\phi$. We
show that the dimensions of moduli spaces of embedded pseudoholomorphic curves
in $\R\times Y$, with cylindrical ends asymptotic to periodic orbits of $\phi$
or multiple covers thereof, are bounded from above by an additive relative
index. We deduce some compactness results for these moduli spaces.
  This paper establishes some of the foundations for a program with Michael
Thaddeus, to understand the Seiberg-Witten Floer homology of $Y$ in terms of
such pseudoholomorphic curves. Analogues of our results should also hold in
three dimensional contact homology.
