Translator Disclaimer
2018 Goldman algebra, opers and the swapping algebra
François Labourie
Geom. Topol. 22(3): 1267-1348 (2018). DOI: 10.2140/gt.2018.22.1267

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 ( ) –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 the Wolpert formula.

Citation

Download Citation

François Labourie. "Goldman algebra, opers and the swapping algebra." Geom. Topol. 22 (3) 1267 - 1348, 2018. https://doi.org/10.2140/gt.2018.22.1267

Information

Received: 25 July 2014; Revised: 25 October 2016; Accepted: 11 November 2016; Published: 2018
First available in Project Euclid: 31 March 2018

zbMATH: 06864257
MathSciNet: MR3780435
Digital Object Identifier: 10.2140/gt.2018.22.1267

Subjects:
Primary: 32G15
Secondary: 17B63, 32J15

Rights: Copyright © 2018 Mathematical Sciences Publishers

JOURNAL ARTICLE
82 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.22 • No. 3 • 2018
MSP
Back to Top