  If $(X, \omega)$ is a symplectic manifold, and $\Sigma$ is a smooth
symplectic submanifold Poincar\'e dual to a positive multiple of $\omega$, $X
\setminus \Sigma$ admits a compactification as a Liouville domain, which we
then complete to $(W, d\lambda)$.
  Under monotonicity assumptions on $X$ and on $\Sigma$, we construct a chain
complex whose homology computes the Symplectic Homology of $W$. We show the
differential is given in terms of Morse contributions, terms computed from
Gromov-Witten invariants of $X$ relative to $\Sigma$ and terms computed from
the Gromov-Witten invariants of $\Sigma$.
  We use a Morse-Bott model for symplectic homology. Our proof involves
comparing Floer cylinders with punctures to pseudoholomorphic curves in in the
symplectization of the unit normal bundle to $\Sigma$.
