2018/11/01 by Karsten Fritzsch, Fritzsch, Karsten, Chris Kottke +3
Mathematics · #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph)
paper · pdf · doi:10.48550/arxiv.1811.00601
openalex publication_date 2018/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We describe compactifications of the moduli spaces of SU(2) monopoles on R3 as manifolds with corners, with respect to which the hyperKaehler metrics admit asymptotic expansions up to each boundary face. The boundary faces encode monopoles of charge k decomposing into widely separated monopoles of lower charge, and the leading order asymptotic of the metric generalizes the one obtained by Gibbons, Manton and Bielawski in the case of complete decomposition into monopoles of unit charge. From the structure of the compactifications, we prove part of Sen's conjecture for the L2 cohomology of the strongly centered moduli spaces by adapting an argument of Segal and Selby.