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math.GT2026
Topological components of surface group representations into the unitary group
Xueyuan Wan
We study representations of compact oriented surface groups into with elliptic-unipotent boundary holonomies, meaning that no boundary holonomy has eigenvalue . W…
math.GT2026
On possible values of the signature of flat unitary bundles over compact surfaces
Inkang Kim, Pierre Pansu, Xueyuan Wan
We determine all possible signatures of flat Hermitian bundles over compact, connected, oriented surfaces of positive genus with nonempty boundary. If has genus …
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…