A gluing construction for periodic monopoles

Lorenzo Foscolo

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)
21 Downloads (Pure)

Abstract

Cherkis and Kapustin introduced the study of periodic monopoles (with singularities), that is, monopoles on R^2xS^1 possibly singular at a finite collection of points. Four-dimensional moduli spaces of periodic monopoles with singularities are expected to provide examples of gravitational instantons, that is, complete hyperkähler four-manifolds with finite energy. In a previous paper we proved that the moduli space of charge k periodic monopoles with n singularities is either empty or generically a smooth hyperkähler manifold of dimension 4(k-1). In this paper we settle the existence question, constructing periodic monopoles (with singularities) by gluing methods.
Original languageEnglish
Pages (from-to)7504-7550
JournalInternational Mathematics Research Notices
Volume2017
Issue number24
Early online date10 Nov 2016
DOIs
Publication statusPublished - 1 Dec 2017

Fingerprint Dive into the research topics of 'A gluing construction for periodic monopoles'. Together they form a unique fingerprint.

Cite this