2021/03/07 by Ka Ho Wong, Wong, Ka Ho, Yang, Tian
Mathematics · #Geometric and Algebraic Topology #Advanced Combinatorial Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2103.04254
We compute the adjoint twisted Reidemeister torsion for closed oriented hyperbolic 3-manifolds and for hyperbolic 3-manifolds with toroidal boundary. In our formula, we consider the manifold as obtained by doing a Dehn-filling along suitable boundary components of a fundamental shadow link complement, and the formula is in terms of the logarithmic holonomy of the meridians of the boundary components. As an important special case, we also write down a formula of the adjoint twisted Reidemeister torsion for the double of a hyperbolic 3-manifold with totally geodesic boundary in terms of the edge lengths of a geometric ideal triangulation of the manifold. These unexpected formulas were inspired by, and played an important role in, the study of the asymptotic expansion of quantum invariants \citeWY.