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I want to study representation of teichmuller space of surface of genus g in psl(2,R). can you suggest any good references.

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Do you mean "Description of Teichmuller space using representations of the surface group to $PSL(2,R)$"? If so, start with Abikoff's book. – Misha Jan 9 '13 at 13:47
@Misha's guess is probably right, but the OP should pose a well-formed question before s/he expects to get an answer. – Igor Rivin Jan 9 '13 at 15:40

R. Fricke, F. Klein, Vorlesungen über die theorie der automorphen functionen, 1897-1912.

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