Homological stability for spaces of embedded surfaces
arXiv:1304.3006 · doi:10.2140/gt.2017.21.1387
Abstract
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.
64 pages. The argument of the proof of homology stability has been simplified by using a single resolution by discs (before, there was a resolution by arcs and a resolution by discs). Additionally, the section about triviality (now Section 7) has an improved exposition