GOLDMAN ALGEBRA, OPERS AND THE SWAPPING ALGEBRA

Abstract : We define a Poisson Algebra called the swapping algebra 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 SL n (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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https://hal.univ-cotedazur.fr/hal-01329439
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Submitted on : Thursday, June 9, 2016 - 11:24:59 AM
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François Labourie. GOLDMAN ALGEBRA, OPERS AND THE SWAPPING ALGEBRA. 2016. ⟨hal-01329439⟩

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