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Representations in certain Hitchin fibers

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Representations in certain Hitchin fibers
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15
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CC Attribution - NonCommercial - NoDerivatives 4.0 International:
You are free to use, copy, distribute and transmit the work or content in unchanged form for any legal and non-commercial purpose as long as the work is attributed to the author in the manner specified by the author or licensor.
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The moduli space of SL(n,C)-Higgs bundles over a Riemann surface admits a Hitchin fibration over the space of holomorphic differentials on the Riemann surface. In this talk, we focus on Hitchin fibers at (q2,0,...,0), that is, the fibers containing Fuchsian locus. We show a comparison theorem on the length spectrum between surface group representations in such fibers with Fuchsian ones, as a generalization of the SL(2,C) case shown by Deroin and Tholozan.