Reidemeister torsion of a 3-manifold obtained by a Dehn-surgery along the figure-eight knot

2015/06/02 by Teruaki Kitano, Kitano, Teruaki
Biochemistry, Genetics and Molecular Biology · Mathematics · #27 (secondary) #57M (primary) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #dental development and anomalies

paper · pdf · doi:10.48550/arxiv.1506.00712

openalex publication_date 2015/06/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let M be a closed 3-manifold obtained by Dehn surgery along the figure-eight knot. We give a formula of the Reisdemeisiter torsion of M for any irreducible SL(2;C)-representation. It is described as a rational expression of the trace of the image of the meridian.

Related

• Some numerical computations on Reidemeister torsion for homology 3-spheres obtained by Dehn surgeries along the figure-eight knot
• Reidemeister torsion and Dehn surgery on twist knots
• A polynomial defined by the SL(2;C)-Reidemeister torsion for a homology 3-sphere obtained by a Dehn surgery along a (2p,q)-torus knot
• A polynomial defined by the SL(2;ℂ)-Reidemeister torsion for a homology 3-sphere obtained by Dehn-surgery along a torus knot
• Reidemeister torsion, hyperbolic three-manifolds, and character varieties