Configuration-mapping spaces and homology stability
arXiv:2007.11607 · doi:10.1007/s40687-021-00270-7
Abstract
For a given bundle over a manifold, configuration-section spaces on parametrise finite subsets equipped with a section of defined on , with prescribed "charge" in a neighbourhood of the points . These spaces may be interpreted physically as spaces of fields that are permitted to be singular at finitely many points, with constrained behaviour near the singularities. As a special case, they include the Hurwitz spaces, which parametrise branched covering spaces of the -disc with specified deck transformation group. We prove that configuration-section spaces are homologically stable (with integral coefficients) whenever the underlying manifold is connected and has non-empty boundary and the charge is "small" in a certain sense. This has a partial intersection with the work on Hurwitz spaces of Ellenberg, Venkatesh and Westerland.
arXiv comment37 pages, 11 figures. Final accepted version, to appear in Res. Math. Sci. Section 10 has been removed and will be revised and appear separately. Section 9 has been merged into sections 7 and 8
References in corpus (12)
- Deformation quantization of Poisson manifolds, I
- Homological stability for unordered configuration spaces
- Homological stability for Hurwitz spaces and the Cohen-Lenstra conjecture over function fields, II
- Twisted homological stability for configuration spaces
- Homological stability of topological moduli spaces
- Homological stability for oriented configuration spaces
- (Non-)formality of the extended Swiss Cheese operads
- Improved homological stability for configuration spaces after inverting 2
- Tubular configurations: equivariant scanning and splitting
- Homological stability for moduli spaces of disconnected submanifolds, I
- A comparison of twisted coefficient systems
- Formality of a higher-codimensional Swiss-Cheese operad