Topological components of surface group representations and signature

Inkang Kim; Xueyuan Wan

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arXiv · 2508.05000

Topological components of surface group representations and signature

Inkang Kim·Xueyuan Wan

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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 [14], we determine the number of connected components of the representation spaces with boundary elliptic, hyperbolic, and parabolic holonomies.

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Inkang Kim, Xueyuan Wan. 2025-08-07. Topological components of surface group representations and signature. https://arxiv.org/abs/2508.05000

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