  We study topological properties of log-symplectic structures and produce
examples of compact manifolds with such structures. Notably we show that
several symplectic manifolds do not admit log-symplectic structures and several
log-symplectic manifolds do not admit symplectic structures, for example #m
CP^2 # n bar(CP^2)$ has log-symplectic structures if and only if m,n>0 while
they only have symplectic structures for m=1. We introduce surgeries that
produce log-symplectic manifolds out of symplectic manifolds and show that for
any simply connected 4-manifold M, the manifolds M # (S^2 \times S^2) and M #
CP^2 # CP^2bar have log-symplectic structures and any compact oriented
log-symplectic four-manifold can be transformed into a collection of symplectic
manifolds by reversing these surgeries.
