Configuration-section spaces parametrise fields with singularities on a given manifold, and may be viewed as an enrichment of configuration spaces by non-local data. Hurwitz spaces are two-dimensional examples of these, parametrising branched coverings of surfaces, and the behaviour of their homology is important for questions in analytic number theory, as shown in a celebrated result of Ellenberg, Venkatesh and Westerland on the Cohen-Lenstra conjecture. I will talk about joint work with Ulrike Tillmann (some published and some in progress) on homological stability and the stable homology of configuration-section spaces. Time permitting, I will also explain how similar techniques may be applied to asymptotic monopole moduli spaces. |
Links:
[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/node/10868