Some numerical computations on Reidemeister torsion for homology 3-spheres obtained by Dehn surgeries along the figure-eight knot

TL;DR

This paper presents computations of Reidemeister torsion for homology 3-spheres derived from Dehn surgeries on the figure-eight knot, focusing on SL(2;C) representations of their fundamental groups.

Contribution

It provides detailed numerical computations of Reidemeister torsion for specific 3-spheres, improving accuracy through correction of previous errors.

Findings

Reidemeister torsion values for these 3-spheres are explicitly calculated.

SL(2;C) representations of the fundamental group are analyzed.

The results enhance understanding of topological invariants in knot surgery contexts.

Abstract

We show some computations on representations of the fundamental group in SL(2;C) and Reidemeister torsion for a homology 3-sphere obtained by Dehn surgery along the figure-eight knot. This is the second version. We recorrected several errors in the first version.