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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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2016 |
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Інститут математики НАН України
2016
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/147753 |
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| Zitieren: | 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| _version_ | 1862725848958763008 |
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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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| first_indexed | 2025-12-07T18:54:25Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-147753 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T18:54:25Z |
| publishDate | 2016 |
| 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 |