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Fenchel–Nielsen coordinates and Goldman brackets
L. O. Chekhov Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
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 $\Sigma_{g,s}$ with holes. These structures are generalized to the case of Riemann surfaces $\Sigma_{g,s,n}$ with holes and bordered cusps.
Bibliography: 49 titles.
Keywords:
Darboux coordinates, Teichmüller spaces, Poisson structure, geodesics.
Received: 30.07.2020
Citation:
L. O. Chekhov, “Fenchel–Nielsen coordinates and Goldman brackets”, Uspekhi Mat. Nauk, 75:5(455) (2020), 153–190; Russian Math. Surveys, 75:5 (2020), 929–964
Linking options:
https://www.mathnet.ru/eng/rm9972https://doi.org/10.1070/RM9972 https://www.mathnet.ru/eng/rm/v75/i5/p153
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Abstract page: | 313 | Russian version PDF: | 53 | English version PDF: | 34 | References: | 35 | First page: | 19 |
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