The asymptotics of the higher dimensional Reidemeister torsion for exceptional surgeries along twist knots

TL;DR

This paper analyzes the asymptotic behavior of higher dimensional Reidemeister torsion in graph manifolds created by exceptional surgeries on twist knots, revealing the structure of irreducible representations and explicit limit sets.

Contribution

It establishes the asymptotic behavior of Reidemeister torsion for these manifolds and characterizes the induced representations, providing explicit limits of torsion coefficients.

Findings

All irreducible SL(2;C)-representations are induced by irreducible metabelian representations.

Explicit set of limits for the leading coefficients in Reidemeister torsion.

Asymptotic formulas for torsion in the context of exceptional surgeries on twist knots.

Abstract

We determine the asymptotic behavior of the higher dimensional Reidemeister torsion for the graph manifolds obtained by exceptional surgeries along twist knots. We show that all irreducible SL(2;C)-representations of the graph manifold are induced by irreducible metabelian representations of the twist knot group. We also give the set of the limits of the leading coefficients in the higher dimensional Reidemeister torsion explicitly.