Homological stability for spaces of embedded surfaces
Geometry and Topology
Mathematical Sciences Publisher
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Morán, F., & Randal-Williams, O. (2017). Homological stability for spaces of embedded surfaces. Geometry and Topology, 21 (3), 1387-1467. https://doi.org/10.2140/gt.2017.21.1387
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–dimensional submanifolds to 2–dimensional submanifolds.
External DOI: https://doi.org/10.2140/gt.2017.21.1387
This record's URL: https://www.repository.cam.ac.uk/handle/1810/266065