Moduli spaces of local systems and higher Teichmuller theory

@misc{citeulike:142875, abstract = {Let G be a split semisimple algebraic group. Let S be a compact 2D surface with boundary. We defined two moduli spaces closely related to the moduli spaces of G-local systems on S. We show that they carry a lot of interesting structures. In particular we define a distinguished collection of coordinate systems, equivariant under the action of the mapping class group of S. We prove that their transition functions are subtraction free. Thus we have positive structures on these moduli spaces. Therefore we can take their points with values in any positive semifield. Their positive real points provide the two higher Teichmuller spaces related to G and S, while the points with values in the tropical semifields provide the lamination spaces. We define the motivic avatar of the Weil-Petersson form for one of these spaces. It is related to the motivic dilogarithm.}, author = {Fock, V. and Goncharov, A. }, citeulike-article-id = {142875}, eprint = {math.AG/0311149}, keywords = {fock, tropical}, month = {May}, posted-at = {2005-03-30 08:16:41}, priority = {2}, title = {Moduli spaces of local systems and higher Teichmuller theory}, url = {http://arxiv.org/abs/math.AG/0311149}, year = {2004} }

TY - ELEC ID - citeulike:142875 L3 - citeulike-article-id:142875 TI - Moduli spaces of local systems and higher Teichmuller theory N2 - Let G be a split semisimple algebraic group. Let S be a compact 2D surface with boundary. We defined two moduli spaces closely related to the moduli spaces of G-local systems on S. We show that they carry a lot of interesting structures. In particular we define a distinguished collection of coordinate systems, equivariant under the action of the mapping class group of S. We prove that their transition functions are subtraction free. Thus we have positive structures on these moduli spaces. Therefore we can take their points with values in any positive semifield. Their positive real points provide the two higher Teichmuller spaces related to G and S, while the points with values in the tropical semifields provide the lamination spaces. We define the motivic avatar of the Weil-Petersson form for one of these spaces. It is related to the motivic dilogarithm. KW - fock KW - tropical AU - Fock, V AU - Goncharov, A PY - 2004/05/19/ UR - http://arxiv.org/abs/math.AG/0311149 ER -