Singular Instantons and Painlevé VI

We consider a two parameter family of instantons, which is studied in [Sadun L., Comm. Math. Phys. 163 (1994), 257-291], invariant under the irreducible action of SU₂ on S⁴, but which are not globally defined. We will see that these instantons produce solutions to a one parameter family of Painlevé...

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Опубліковано в: :Symmetry, Integrability and Geometry: Methods and Applications
Дата:2016
Автор: Muñiz Manasliski, R.
Формат: Стаття
Мова:Англійська
Опубліковано: Інститут математики НАН України 2016
Онлайн доступ:https://nasplib.isofts.kiev.ua/handle/123456789/147753
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати:Singular Instantons and Painlevé VI / R. Muñiz Manasliski // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 24 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Muñiz Manasliski, R.
author_facet Muñiz Manasliski, R.
citation_txt Singular Instantons and Painlevé VI / R. Muñiz Manasliski // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 24 назв. — англ.
collection DSpace DC
container_title Symmetry, Integrability and Geometry: Methods and Applications
description We consider a two parameter family of instantons, which is studied in [Sadun L., Comm. Math. Phys. 163 (1994), 257-291], invariant under the irreducible action of SU₂ on S⁴, but which are not globally defined. We will see that these instantons produce solutions to a one parameter family of Painlevé VI equations (PVI) and we will give an explicit expression of the map between instantons and solutions to PVI. The solutions are algebraic only for that values of the parameters which correspond to the instantons that can be extended to all of S⁴. This work is a generalization of [Muñiz Manasliski R., Contemp. Math., Vol. 434, Amer. Math. Soc., Providence, RI, 2007, 215-222] and [Muñiz Manasliski R., J. Geom. Phys. 59 (2009), 1036-1047, arXiv:1602.07221], where instantons without singularities are studied.
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publisher Інститут математики НАН України
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spelling Muñiz Manasliski, R.
2019-02-15T19:10:27Z
2019-02-15T19:10:27Z
2016
Singular Instantons and Painlevé VI / R. Muñiz Manasliski // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 24 назв. — англ.
1815-0659
2010 Mathematics Subject Classification: 34M55; 53C07; 53C28
DOI:10.3842/SIGMA.2016.057
https://nasplib.isofts.kiev.ua/handle/123456789/147753
We consider a two parameter family of instantons, which is studied in [Sadun L., Comm. Math. Phys. 163 (1994), 257-291], invariant under the irreducible action of SU₂ on S⁴, but which are not globally defined. We will see that these instantons produce solutions to a one parameter family of Painlevé VI equations (PVI) and we will give an explicit expression of the map between instantons and solutions to PVI. The solutions are algebraic only for that values of the parameters which correspond to the instantons that can be extended to all of S⁴. This work is a generalization of [Muñiz Manasliski R., Contemp. Math., Vol. 434, Amer. Math. Soc., Providence, RI, 2007, 215-222] and [Muñiz Manasliski R., J. Geom. Phys. 59 (2009), 1036-1047, arXiv:1602.07221], where instantons without singularities are studied.
s
 The author would like to thank Nigel Hitchin for his suggestion to look at instantons with
 holonomic singularities and Gil Bor for many useful conversations. We also thank the referees
 for many useful suggestions that help to improve the paper. This work was partially supported
 by Grupo CSIC 618 (UdelaR, Uruguay).
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Singular Instantons and Painlevé VI
Article
published earlier
spellingShingle Singular Instantons and Painlevé VI
Muñiz Manasliski, R.
title Singular Instantons and Painlevé VI
title_full Singular Instantons and Painlevé VI
title_fullStr Singular Instantons and Painlevé VI
title_full_unstemmed Singular Instantons and Painlevé VI
title_short Singular Instantons and Painlevé VI
title_sort singular instantons and painlevé vi
url https://nasplib.isofts.kiev.ua/handle/123456789/147753
work_keys_str_mv AT munizmanasliskir singularinstantonsandpainlevevi