  We study the space of oriented genus g subsurfaces of a fixed manifold M, and
in particular its homological properties. We construct a "scanning map" which
compares this space to the space of sections of a certain fibre bundle over M
associated to its tangent bundle, and show that this map induces an isomorphism
on homology in a range of degrees.
  Our results are analogous to McDuff's theorem on configuration spaces,
extended from 0-manifolds to 2-manifolds.
