Homological stability for spaces of embedded surfaces
(2017) Geometry & Topology — Vol. 21, p. 1387-1467 (2017)
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- 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–dimensional submanifolds to 2–dimensional submanifolds.
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Cantero Moran, F., & Randal-Williams, O. (2017). Homological stability for spaces of embedded surfaces. Geometry & Topology, 21, 1387-1467. https://doi.org/10.2140/gt.2017.21.1387 (Original work published 2017)