Geometry of Moduli Spaces of Flat Bundles on Punctured Surfaces

Details Geometry of Moduli Spaces of Flat Bundles on Punctured Surfaces Geometry of Moduli Spaces of Flat Bundles on Punctured Surfaces

1997-03-05

arxiv.org/abs/alg-geom/9703004v1

Mathematics

Algebraic Geometry

LaTeX, 12 pages

Scientific paper

We consider the moduli spaces of flat $SL(n, C)$-bundles on Riemann surfaces with one puncture when we fix the conjugacy class ${\cal C}$ of the monodromy transformation around the puncture. We show that under a certain condition on the class ${\cal C}$ (namely the product of $k1$ and $A_1A_2\cdots A_pA_1^{-1}A_2^{-1}\cdots A_p^{-1}$ belongs to a class which satisfies property P then the $p$ -tuple $(A_1, ..., A_p)$ algebraically generates the whole group $G$.

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