Goldman algebra, opers and the swapping algebra
We define a Poisson Algebra called the swapping al- gebra using the intersection of curves in the disk. We interpret a subalgebra of the fraction algebra of the swapping algebra – called the algebra of multifractions – as an algebra of functions on the space of cross ratios and thus as an algebra of...
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Veröffentlicht in: | Geometry & topology 2018-03, Vol.22 (3), p.1267-1348 |
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Format: | Artikel |
Sprache: | eng |
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Zusammenfassung: | We define a Poisson Algebra called the swapping al- gebra using the intersection of curves in the disk. We interpret a subalgebra of the fraction algebra of the swapping algebra – called the algebra of multifractions – as an algebra of functions on the space of cross ratios and thus as an algebra of functions on the Hitchin component as well as on the space of SLn(R)-opers with trivial holonomy. We relate this Poisson algebra to the Atiyah– Bott–Goldman symplectic structure and to the Drinfel’d–Sokolov reduction. We also prove an extension of Wolpert formula. |
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ISSN: | 1465-3060 1364-0380 |
DOI: | 10.2140/gt.2018.22.1267 |