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Homological stability for spaces of embedded surfaces

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Cantero Moran, Federico [UCL] Randal-Williams, Oscar

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.

Document type Article de périodique (Journal article) – Article de recherche
Publication date 2017
Language Anglais
Journal information "Geometry & Topology" - Vol. 21, p. 1387-1467 (2017)
Peer reviewed yes
Publisher Mathematical Sciences Publishers
issn 1465-3060
e-issn 1364-0380
Publication status Publié
Affiliation UCL - SST/IRMP - Institut de recherche en mathématique et physique
Keywords Geometry and Topology
Links
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Bibliographic reference Cantero Moran, Federico ; Randal-Williams, Oscar. Homological stability for spaces of embedded surfaces. In: Geometry & Topology, Vol. 21, p. 1387-1467 (2017)
Permanent URL http://hdl.handle.net/2078.1/187860