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math.GT2025
Topological components of surface group representations and signature
Inkang Kim, Xueyuan Wan
We study the topological components of the surface group representations into and . Utilizing the signature formula establis…
math.GT2025
Positivity of simplicial volume for closed nonpositively curved four-manifolds with nonzero Euler characteristic
Inkang Kim, Xueyuan Wan
In this paper, by employing the Gauss-Bonnet theorem for Riemannian simplices due to Allendoerfer and Weil, we show that if a closed nonpositively curved -manifold has nonzero E…