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Autor:	Lawton, Sean
Título:	Poisson geometry of SL (3,C)-character varieties relative to a surface with boundary
Páginas/Colación:	pp. 2397-2429
Fecha:	May 2009

Transactions of the American Mathematical Society Vol. 361, no.5 May 2009

Información de existencia

Resumen
We construct different types of quasiperiodically forced circle homeomorphisms with transitive but non-minimal dynamics

The $\mathrm{SL}(3,\mathbb{C})$ -representation variety $\mathfrak{R}$ of a free group $\mathtt{F}_r$ arises naturally by considering surface group representations for a surface with boundary. There is an $\mathrm{SL}(3,\mathbb{C})$ -action on the coordinate ring of $\mathfrak{R}$ by conjugation. The geometric points of the subring of invariants of this action is an affine variety $\mathfrak{X}$ . The points of $\mathfrak{X}$ parametrize isomorphism classes of completely reducible representations. We show the coordinate ring $\mathbb{C}[\mathfrak{X}]$ is a complex Poisson algebra with respect to a presentation of $\mathtt{F}_r$ imposed by the surface. Lastly, we work out the bracket on all generators when the surface is a three-holed sphere or a one-holed torus.

UCLA - Biblioteca de Ciencias y Tecnologia Felix Morales Bueno

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