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Adjoint twisted Reidemeister torsion and Gram matrices by Wong, Ka Ho; Yang, Tian is a scholarly article available to read on EtoBox.

What is Adjoint twisted Reidemeister torsion and Gram matrices about?

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\,\cite{WY}.

Author

Wong, Ka Ho; Yang, Tian

Published

2021

Language

EN