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Topological components of surface group representations and the signature (2508.05000v1)
Published 7 Aug 2025 in math.GT and math.RT
Abstract: We study the topological components of the surface group representations into $\mathrm{SL}(2,\mathbb{R})$ and $\mathrm{PSL}(2,\mathbb{R})$. Utilizing the signature formula established in [10], we determine the number of connected components of the representation spaces with boundary elliptic, hyperbolic, and parabolic holonomies.
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