Deformation Theory of Periodic Monopoles (With Singularities)

Lorenzo Foscolo

doi:10.1007/s00220-015-2497-3

Deformation Theory of Periodic Monopoles (With Singularities)

Lorenzo Foscolo

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Abstract

Cherkis and Kapustin (Commun Math Phys 218(2): 333–371, 2001 and Commun Math Phys 234(1):1–35, 2003) introduced periodic monopoles (with singularities), i.e. monopoles on R^2xS^1 possibly singular at a finite collection of points. In this paper we show that for generic choices of parameters the moduli spaces of periodic monopoles (with singularities) with structure group SO(3) are either empty or smooth hyperkähler manifolds. Furthermore, we prove an index theorem and therefore compute the dimension of the moduli spaces.

Original language	English
Pages (from-to)	351–390
Number of pages	40
Journal	Communications in Mathematical Physics
Volume	341
Issue number	1
DOIs	https://doi.org/10.1007/s00220-015-2497-3
Publication status	Published - Jan 2016

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This is a post-peer-review, pre-copyedit version of an article published in Communications in Mathematical Physics. The final authenticated version is available online at: http://dx.doi.org/10.1007/s00220-015-2497-3
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abstract = "Cherkis and Kapustin (Commun Math Phys 218(2): 333–371, 2001 and Commun Math Phys 234(1):1–35, 2003) introduced periodic monopoles (with singularities), i.e. monopoles on R^2xS^1 possibly singular at a finite collection of points. In this paper we show that for generic choices of parameters the moduli spaces of periodic monopoles (with singularities) with structure group SO(3) are either empty or smooth hyperk{\"a}hler manifolds. Furthermore, we prove an index theorem and therefore compute the dimension of the moduli spaces.",

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JO - Communications in Mathematical Physics

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Deformation Theory of Periodic Monopoles (With Singularities)

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