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Homological Stability for Spaces of Embedded Surfaces

dc.creatorMoran, Federico Cantero
dc.creatorRandal-Williams, Oscar
dc.date.accessioned2016-05-30
dc.date.accessioned2018-11-24T23:26:48Z
dc.date.available2016-06-27T13:57:11Z
dc.date.available2018-11-24T23:26:48Z
dc.date.issued2016
dc.identifierhttps://www.repository.cam.ac.uk/handle/1810/256496
dc.identifier.urihttp://repository.aust.edu.ng/xmlui/handle/123456789/3888
dc.description.abstractWe study the space of oriented genus $\textit{g}$ subsurfaces of a fixed manifold $\textit{M}$, 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 $\textit{M}$ 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.
dc.languageen
dc.publisherMathematical Sciences Publisher
dc.publisherGeometry & Topology
dc.titleHomological Stability for Spaces of Embedded Surfaces
dc.typeArticle


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