Homology stability for asymptotic monopole moduli spaces

TL;DR

This paper establishes homological stability for two types of asymptotic monopole moduli spaces, expanding understanding of their topological properties and boundary structures in monopole theory.

Contribution

It proves homological stability for asymptotic monopole moduli spaces, including framed Dirac monopoles and ideal monopoles, using a general stability result for configuration spaces with non-local data.

Findings

Homological stability holds for framed Dirac monopole moduli spaces.

Homological stability also applies to ideal monopole moduli spaces.

Results provide insights into the boundary structures of monopole moduli spaces.

Abstract

We prove homological stability for two different flavours of asymptotic monopole moduli spaces, namely moduli spaces of framed Dirac monopoles and moduli spaces of ideal monopoles. The former are Gibbons-Manton torus bundles over configuration spaces whereas the latter are obtained from them by replacing each circle factor of the fibre with a monopole moduli space by the Borel construction. They form boundary hypersurfaces in a partial compactification of the classical monopole moduli spaces. Our results follow from a general homological stability result for configuration spaces equipped with non-local data.