Geometry & Topology
- Geom. Topol.
- Volume 21, Number 3 (2017), 1387-1467.
Homological stability for spaces of embedded surfaces
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.
Geom. Topol., Volume 21, Number 3 (2017), 1387-1467.
Received: 14 July 2014
Revised: 14 March 2016
Accepted: 29 May 2016
First available in Project Euclid: 16 November 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 55R40: Homology of classifying spaces, characteristic classes [See also 57Txx, 57R20] 57R20: Characteristic classes and numbers 57R40: Embeddings 57R50: Diffeomorphisms 57S05: Topological properties of groups of homeomorphisms or diffeomorphisms
Cantero, Federico; Randal-Williams, Oscar. Homological stability for spaces of embedded surfaces. Geom. Topol. 21 (2017), no. 3, 1387--1467. doi:10.2140/gt.2017.21.1387. https://projecteuclid.org/euclid.gt/1510859205