Abstract
We show that any representation of the fundamental group of an orientable surface Σ in GLn(R) admits a base of neighborhoods in any of which the subset of irreducible representations is a pathwise connected and dense subset, as long as the genus of Σ is big enough.
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Guichard, O. Connexite et densite des representations irreductibles des groupes de surface dans le groupe general lineaire. Transformation Groups 12, 251–292 (2007). https://doi.org/10.1007/s00031-006-0038-z
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DOI: https://doi.org/10.1007/s00031-006-0038-z