Fenchel--Nielsen coordinates and Goldman brackets

2020/08/28 by Chekhov, Leonid O. · 1 citation
#51H25 #FOS: Mathematics #FOS: Physical sciences #Geometric Topology (math.GT) #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2008.12777

Abstract

We explicitly show that the Poisson bracket on the set of shear coordinates introduced by V.V. Fock in 1997 induces the Fenchel--Nielsen bracket on the set of gluing parameters (length and twist parameters) for pairs of pants decomposition for Riemann surfaces with holes Σ_g,s. We generalize these structures to the case of Riemann surfaces Σ_g,s,n with holes and bordered cusps.

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