%0 Journal Article
%T Homological stability for spaces of embedded surfaces
%A Federico Cantero
%A Oscar Randal-Williams
%J Mathematics
%D 2013
%I arXiv
%X 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.
%U http://arxiv.org/abs/1304.3006v2