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Generators of the homological Goldman Lie algebra. (English) Zbl 1301.57014
Summary: We determine the minimum number of generators of the homological Goldman Lie algebra of a surface consisting of elements of the first homology group of the surface.
MSC:
57M99 General low-dimensional topology
57N05 Topology of the Euclidean \(2\)-space, \(2\)-manifolds (MSC2010)
17B65 Infinite-dimensional Lie (super)algebras
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References:
[1] W.M. Goldman: Invariant functions on Lie groups and Hamiltonian flows of surface group representations , Invent. Math. 85 (1986), 263-302. · Zbl 0619.58021 · doi:10.1007/BF01389091 · eudml:143369
[2] S.P. Humphries: Generators for the mapping class group ; in Topology of Low-Dimensional Manifolds (Proc. Second Sussex Conf., Chelwood Gate, 1977), Lecture Notes in Math. 722 , Springer, Berlin, 1979, 44-47. · Zbl 0732.57004 · doi:10.1007/BFb0063188
[3] K. Toda: The ideals of the homological Goldman Lie algebra , to appear in Kodai Math. J., available at arXiv: · Zbl 1328.17008 · doi:10.2996/kmj/1372337512 · arxiv.org
[4] V.G. Turaev: Skein quantization of Poisson algebras of loops on surfaces , Ann. Sci. École Norm. Sup. (4) 24 (1991), 635-704. \endthebibliography* · Zbl 0758.57011 · numdam:ASENS_1991_4_24_6_635_0 · eudml:82308
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