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The renormalization of volume and Chern-Simons invariant for hyperbolic 3-manifolds
- Publication Year :
- 2023
-
Abstract
- 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 Weitzenb\"ock 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.<br />Comment: 42 pages, 2 figures
- Subjects :
- Mathematics - Differential Geometry
58J28, 57K32
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2310.04776
- Document Type :
- Working Paper