3 papers
math.DG2026
The Asymptotic Structure of Monopoles in R^3, Calorons, and ALF Instantons
Sergey A. Cherkis, Mark Stern
We study the asymptotic structure of instantons on multi-centered Taub-NUT manifolds, calorons, and monopoles on R^3. We show that, without any assumptions on symmetry breaking, th…
math.DG2025
Instantons on multi-Taub-NUT Spaces III: Down Transform, Completeness, and Isometry
Sergey A. Cherkis, Andrés LarraÃn-Hubach, Mark Stern
The index bundle of a family of Dirac operators associated to an instanton on a multi-Taub-NUT space forms a bow representation. We prove that the gauge equivalence classes of solu…
math.DG2024
Harmonic Forms, Price Inequalities, and Benjamini-Schramm Convergence
Luca F. Di Cerbo, Mark Stern
We study Betti numbers of sequences of Riemannian manifolds which Benjamini-Schramm converge to their universal covers. Using the Price inequalities we developed elsewhere, we deri…