3 papers
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…
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.GR2024
On possible values of the signature of flat symplectic bundles over surfaces with boundary
Inkang Kim, Pierre Pansu, Xueyuan Wan
We show that every integer in the interval is achieved by the signature of a rank flat symplectic bundle over a surface with boundary . When ,…