An algebraic proof for the symplectic structure of moduli space
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- by Yael Karshon PDF
- Proc. Amer. Math. Soc. 116 (1992), 591-605 Request permission
Abstract:
Goldman has constructed a symplectic form on the moduli space $\operatorname {Hom} (\pi ,G)/G$, of flat $G$-bundles over a Riemann surface $S$ whose fundamental group is $\pi$. The construction is in terms of the group cohomology of $\pi$. The proof that the form is closed, though, uses de Rham cohomology of the surface $S$, with local coefficients. This symplectic form is shown here to be the restriction of a tensor, that is defined on the infinite product space ${G^\pi }$. This point of view leads to a direct proof of the closedness of the form, within the language of group cohomology. The result applies to all finitely generated groups $\pi$ whose cohomology satisfies certain conditions. Among these are the fundamental groups of compact Kähler manifolds.References
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Additional Information
- © Copyright 1992 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 116 (1992), 591-605
- MSC: Primary 14D22; Secondary 32G13, 55N99, 57R15, 58F05
- DOI: https://doi.org/10.1090/S0002-9939-1992-1112494-2
- MathSciNet review: 1112494