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Homological stability for
spaces of embedded surfaces
Federico Cantero Morán and Oscar Randal-Williams |
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Geometry & Topology 21 (2017) 1387–1467
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Abstract |
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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. |
Keywords
submanifolds, characteristic classes, homology stability,
embedding spaces, mapping class groups, scanning
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Mathematical Subject Classification 2010
Primary: 55R40, 57R20, 57R40, 57R50, 57S05
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References |
Publication
Received: 14 July 2014
Revised: 14 March 2016
Accepted: 29 May 2016
Published: 10 May 2017
Proposed: Shigeyuki Morita
Seconded: Peter Teichner, Benson Farb
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Authors |
| Federico Cantero Morán | |
| Institut de Recherche en
Mathématique et Physique Université Catholique de Louvain Chemin du Cyclotron, 2 1348 Louvain-la-Neuve Belgium |
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| Oscar Randal-Williams | |
| Centre for Mathematical
Sciences University of Cambridge Wilberforce Road Cambridge CB3 0WB United Kingdom |
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