Osaka Journal of Mathematics

Generators of the homological Goldman Lie algebra

Nariya Kawazumi, Yusuke Kuno, and Kazuki Toda

Full-text: Open access

Abstract

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.

Article information

Source
Osaka J. Math., Volume 51, Number 3 (2014), 665-673.

Dates
First available in Project Euclid: 23 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.ojm/1414090797

Mathematical Reviews number (MathSciNet)
MR3272611

Zentralblatt MATH identifier
1301.57014

Subjects
Primary: 57N05: Topology of $E^2$ , 2-manifolds 17B65: Infinite-dimensional Lie (super)algebras [See also 22E65]

Citation

Kawazumi, Nariya; Kuno, Yusuke; Toda, Kazuki. Generators of the homological Goldman Lie algebra. Osaka J. Math. 51 (2014), no. 3, 665--673. https://projecteuclid.org/euclid.ojm/1414090797


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References

  • W.M. Goldman: Invariant functions on Lie groups and Hamiltonian flows of surface group representations, Invent. Math. 85 (1986), 263–302.
  • 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.
  • K. Toda: The ideals of the homological Goldman Lie algebra, to appear in Kodai Math. J., available at arXiv:1112.1213.
  • V.G. Turaev: Skein quantization of Poisson algebras of loops on surfaces, Ann. Sci. École Norm. Sup. (4) 24 (1991), 635–704. \endthebibliography*