On the variation of the Poisson structures of certain moduli spaces

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• 作者：Johannes Huebschmann
• 关键词：Mathematics Subject Classification (1991) ; 53C07 ; 53D17 ; 53D20 ; 53D30 ; 58D27 ; 58E15 ; 32G13 ; 53D50 ; 81S10 ; 81T13.
• 刊名：Mathematische Annalen
• 出版年：2001
• 出版时间：February 2001
• 年：2001
• 卷：319
• 期：2
• 页码：267-310
• 全文大小：329 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-1807

文摘

Let be the fundamental group of a compact connected orientable topological surface with finitely many boundary circles. Our aim is to construct Poisson algebras of continuous functions on certain open subspaces of the space of representations of in a Lie group G whose Lie algebra is supposed to be endowed with a nondegenerate invariant symmetric bilinear form. When G is compact and connected, the spaces may be taken to be dense in the space of all representations. The spaces contain spaces of representations where the values of those generators of the fundamental group which correspond to the boundary circles are constrained to lie in fixed conjugacy classes and, the representation spaces being endowed with universal Poisson algebras constructed elsewhere earlier, the restrictions from the spaces to any of the spaces are Poisson maps. Thus the Poisson algebra on each gives a description of the variation of the universal Poisson structures on the spaces as the chosen conjugacy classes move across G. We also give twisted versions of these results.