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Russian Mathematical Surveys, 2020, Volume 75, Issue 5, Pages 929–964
DOI: https://doi.org/10.1070/RM9972 (Mi rm9972) 		 
Fenchel–Nielsen coordinates and Goldman brackets

L. O. Chekhov

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
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DOI: https://doi.org/10.1070/RM9972
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.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-15-2019-1614
This work was performed at the Steklov International Mathematical Center and supported by the Ministry of Science and Higher Education of the Russian Federation (agreement no. 075-15-2019-1614).
Received: 30.07.2020
Russian version:
Uspekhi Matematicheskikh Nauk, 2020, Volume 75, Issue 5(455), Pages 153–190
DOI: https://doi.org/10.4213/rm9972
Bibliographic databases:
Document Type: Article
UDC: 514.7+512.548
MSC: Primary 30F60, 57K20; Secondary 32G15
Language: English
Original paper language: Russian
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
Citation in format AMSBIB
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