Abstract
In this note we prove that the number of irreducible components of Hom (π,G) is the same as π1(G), where π is a surface group andG is complex semisimple. This is established by studying the flat bundles on Riemann surfaces.
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The present work is partially supported by NSF grant DMS89-04922
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Li, J. The space of surface group representations. Manuscripta Math 78, 223–243 (1993). https://doi.org/10.1007/BF02599310
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DOI: https://doi.org/10.1007/BF02599310