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
1. Verfasser: Labourie, François
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.
ISSN:1465-3060
1364-0380
DOI:10.2140/gt.2018.22.1267