Reidemeister torsion and Dehn surgery on twist knots

TL;DR

This paper calculates Reidemeister torsion for twist knot complements and the resulting 3-manifolds after Dehn surgery, providing insights into their topological invariants.

Contribution

It introduces explicit computations of Reidemeister torsion for twist knots and their Dehn surgeries, advancing understanding of their topological properties.

Findings

Explicit formulas for Reidemeister torsion of twist knot complements.

Reidemeister torsion of 3-manifolds after Dehn surgery on twist knots.

Enhanced understanding of topological invariants of these manifolds.

Abstract

We compute the Reidemeister torsion of the complement of a twist knot in $S^3$ and that of the 3-manifold obtained by a Dehn surgery on a twist knot.