Fenchel–Nielsen coordinates and Goldman brackets

Abstract

Abstract It is explicitly shown that the Poisson bracket on the set of shear coordinates defined by V. V. Fock in 1997 induces the Fenchel–Nielsen bracket on the set of gluing parameters (length and twist parameters) for pair-of-pants decompositions of Riemann surfaces with holes. These structures are generalized to the case of Riemann surfaces with holes and bordered cusps. Bibliography: 49 titles.