A relationship between the non-acyclic Reidemeister torsion and a zero of the acyclic Reidemeister torsion

Yoshikazu Yamaguchi

doi:10.5802/aif.2352

A relationship between the non-acyclic Reidemeister torsion and a zero of the acyclic Reidemeister torsion

Yoshikazu Yamaguchi^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

14 Citations (Scopus)

Abstract

We show a relationship between the non-acyclic Reidemeister torsion and a zero of the acyclic Reidemeister torsion for a λ-regular SU(2) or SL(2, Cℂ)-representation of a knot group. Then we give a method to calculate the non-acyclic Reidemeister torsion of a knot exterior. We calculate a new example and investigate the behavior of the non-acyclic Reidemeister torsion associated to a 2-bridge knot and SU(2)-representations of its knot group.

Original language	English
Pages (from-to)	337-362+IX
Journal	Annales de l'Institut Fourier
Volume	58
Issue number	1
DOIs	https://doi.org/10.5802/aif.2352
Publication status	Published - 2008
Externally published	Yes

Keywords

Knots
Reidemeister torsion
Representation spaces
Twisted Alexander invariant

ASJC Scopus subject areas

Algebra and Number Theory
Geometry and Topology

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10.5802/aif.2352

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AB - We show a relationship between the non-acyclic Reidemeister torsion and a zero of the acyclic Reidemeister torsion for a λ-regular SU(2) or SL(2, Cℂ)-representation of a knot group. Then we give a method to calculate the non-acyclic Reidemeister torsion of a knot exterior. We calculate a new example and investigate the behavior of the non-acyclic Reidemeister torsion associated to a 2-bridge knot and SU(2)-representations of its knot group.

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KW - Representation spaces

KW - Twisted Alexander invariant

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A relationship between the non-acyclic Reidemeister torsion and a zero of the acyclic Reidemeister torsion

Abstract

Keywords

ASJC Scopus subject areas

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