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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Інститут математики НАН України
2016
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| Schriftenreihe: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Zugang: | http://dspace.nbuv.gov.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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irk-123456789-1477532019-02-16T01:26:16Z Singular Instantons and Painlevé VI Muñiz Manasliski, R. 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. 2016 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/147753 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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English |
| 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. |
| format |
Article |
| author |
Muñiz Manasliski, R. |
| spellingShingle |
Muñiz Manasliski, R. Singular Instantons and Painlevé VI Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Muñiz Manasliski, R. |
| author_sort |
Muñiz Manasliski, R. |
| title |
Singular Instantons and Painlevé VI |
| title_short |
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_sort |
singular instantons and painlevé vi |
| publisher |
Інститут математики НАН України |
| publishDate |
2016 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147753 |
| citation_txt |
Singular Instantons and Painlevé VI / R. Muñiz Manasliski // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 24 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT munizmanasliskir singularinstantonsandpainlevevi |
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2025-07-11T02:46:24Z |
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2025-07-11T02:46:24Z |
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