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Hyperbolic monopoles, JNR data and spectral curves

Bolognesi, S.; Cockburn, A.; Sutcliffe, P.M.

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S. Bolognesi

A. Cockburn


A large class of explicit hyperbolic monopole solutions can be obtained from JNR instanton data, if the curvature of hyperbolic space is suitably tuned. Here we provide explicit formulae for both the monopole spectral curve and its rational map in terms of JNR data. Examples with platonic symmetry are presented, together with some one-parameter families with cyclic and dihedral symmetries. These families include hyperbolic analogues of geodesics that describe symmetric monopole scatterings in Euclidean space and we illustrate the results with energy density isosurfaces. There is a metric on the moduli space of hyperbolic monopoles, defined using the Abelian connection on the boundary of hyperbolic space, and we provide a simple integral formula for this metric on the space of JNR data.


Bolognesi, S., Cockburn, A., & Sutcliffe, P. (2015). Hyperbolic monopoles, JNR data and spectral curves. Nonlinearity, 28(1), 211-235.

Journal Article Type Article
Acceptance Date Nov 14, 2014
Online Publication Date Dec 15, 2014
Publication Date Jan 1, 2015
Deposit Date Dec 16, 2014
Publicly Available Date Dec 16, 2014
Journal Nonlinearity
Print ISSN 0951-7715
Electronic ISSN 1361-6544
Publisher IOP Publishing
Peer Reviewed Peer Reviewed
Volume 28
Issue 1
Pages 211-235
Keywords Monopoles, Spectral curves, Instantons.


Accepted Journal Article (1 Mb)

Copyright Statement
© 2014 IOP Publishing Ltd. This is an author-created, un-copyedited version of an article accepted for publication in Nonlinearity. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at

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