Homological stability for spaces of embedded surfaces
Accepted version
Peer-reviewed
Repository URI
Repository DOI
Change log
Authors
Morán, FC
Randal-Williams, Oscar https://orcid.org/0000-0002-7479-2878
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-manifolds to 2-manifolds.
Description
Keywords
math.AT, math.AT, 57R40, 57R50, 57R20, 57S05, 55R40
Journal Title
Geometry and Topology
Conference Name
Journal ISSN
1465-3060
1364-0380
1364-0380
Volume Title
21
Publisher
Mathematical Sciences Publishers
Publisher DOI
Sponsorship
F. Cantero Moran was funded through FPI Grant BES-2008-002642 and by Michael Weiss Humboldt professor grant. He was partially supported by project MTM2013-42178-P funded by the Spanish Ministry of Economy. O. Randal-Williams was supported by ERC Advanced Grant No. 228082, the Danish National Research Foundation through the Centre for Symmetry and Deformation, and the Herchel Smith Fund.