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The Goldman Lie algebra and Kontsevich's ''associative'' formal symplectic geometry

Nariya Kawazumi
(University of Tokyo)
Seminar
Tirsdag, 28 september, 2010, at 16:15-17:15, in Aud. D3 (1531-215)
Abstrakt:
Let \Sigma_{g,1} be a compact connected oriented surface of genus g (\geq 1) with one boundary component, \pi the fundamental group of the surface \Sigma_{g,1}. We prove any symplectic expansion of the group \pi in the sense of Massuyeau induces a natural homomorphism of the Goldman Lie algebra of the surface \Sigma_{g,1} to an extension of Kontsevich's ''associative'' Lie algebra. As applications, we obtain an explicit escription of the action of Dehn twists on the completed group ring of the group \pi, and compute the center of the Goldman Lie algebra of the surface \Sigma_{\infty,1} = \varinjlim_{g\to\infty}\Sigma_{g,1}.

This talk is based on a joint work with Yusuke Kuno (Hiroshima University, JSPS)

Organiseret af: CTQM/QGM
Kontaktperson: Jørgen Ellegaard Andersen