Abstract
We study the space of oriented genus- subsurfaces of a fixed manifold 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 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 –dimensional submanifolds to –dimensional submanifolds.
Citation
Federico Cantero. Oscar Randal-Williams. "Homological stability for spaces of embedded surfaces." Geom. Topol. 21 (3) 1387 - 1467, 2017. https://doi.org/10.2140/gt.2017.21.1387
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