2023/10/07 by Dongha Lee, Lee, Dongha
Mathematics · #57K32 #58J28 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.2310.04776
openalex publication_date 2023/10/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We renormalize the Chern-Simons invariant for convex-cocompact hyperbolic 3-manifolds by finding the asymptotics along an equidistance foliation. We prove that the metric Chern-Simons invariant has an exponentially divergent term given by the integral of the torsion 2-form with respect to a Weitzenböck connection. This produces the asymptotics of hyperbolic volume plus the metric Chern-Simons invariant, which is often called complex volume. The leading coefficient of the asymptotics introduces a complex-valued quantity consisting of mean curvature and torsion 2-form, which is defined on smooth surfaces embedded in a Riemann-Cartan 3-manifold.