Aarhus University Seal / Aarhus Universitets segl

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

Nariya Kawazumi
(University of Tokyo)
Tuesday, 28 September, 2010, at 16:15-17:15, in Aud. D3 (1531-215)

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)

Organised by: CTQM/QGM
Contact person: Jørgen Ellegaard Andersen