Limit values of the nonacyclic reidemeister torsion for knots

Yoshikazu Yamaguchi

doi:10.2140/agt.2007.7.1485

Limit values of the nonacyclic reidemeister torsion for knots

Yoshikazu Yamaguchi^*

^*Corresponding author for this work

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

3 Citations (Scopus)

Abstract

We consider the Reidemeister torsion associated with SL₂(C)-representations of a knot group. A bifurcation point in the SL₂(C)-character variety of a knot group is a character which is given by both an abelian SL₂(C)-representation and a nonabelian one. We show that there exist limits of the nonacyclic Reidemeister torsion at bifurcation points and the limits are expressed by using the derivation of the Alexander polynomial of the knot in this paper.

Original language	English
Pages (from-to)	1485-1507
Number of pages	23
Journal	Algebraic and Geometric Topology
Volume	7
Issue number	1
DOIs	https://doi.org/10.2140/agt.2007.7.1485
Publication status	Published - 2007
Externally published	Yes

Keywords

Character varieties
Knots
Reidemeister torsion
Twisted alexander invariant

ASJC Scopus subject areas

Geometry and Topology

Access to Document

10.2140/agt.2007.7.1485

Cite this

@article{80ca5decd3c84d6d8667333b811fe47c,

title = "Limit values of the nonacyclic reidemeister torsion for knots",

abstract = "We consider the Reidemeister torsion associated with SL2(C)-representations of a knot group. A bifurcation point in the SL2(C)-character variety of a knot group is a character which is given by both an abelian SL2(C)-representation and a nonabelian one. We show that there exist limits of the nonacyclic Reidemeister torsion at bifurcation points and the limits are expressed by using the derivation of the Alexander polynomial of the knot in this paper.",

keywords = "Character varieties, Knots, Reidemeister torsion, Twisted alexander invariant",

author = "Yoshikazu Yamaguchi",

year = "2007",

doi = "10.2140/agt.2007.7.1485",

language = "English",

volume = "7",

pages = "1485--1507",

journal = "Algebraic and Geometric Topology",

issn = "1472-2747",

publisher = "Agriculture.gr",

number = "1",

}

TY - JOUR

T1 - Limit values of the nonacyclic reidemeister torsion for knots

AU - Yamaguchi, Yoshikazu

PY - 2007

Y1 - 2007

N2 - We consider the Reidemeister torsion associated with SL2(C)-representations of a knot group. A bifurcation point in the SL2(C)-character variety of a knot group is a character which is given by both an abelian SL2(C)-representation and a nonabelian one. We show that there exist limits of the nonacyclic Reidemeister torsion at bifurcation points and the limits are expressed by using the derivation of the Alexander polynomial of the knot in this paper.

AB - We consider the Reidemeister torsion associated with SL2(C)-representations of a knot group. A bifurcation point in the SL2(C)-character variety of a knot group is a character which is given by both an abelian SL2(C)-representation and a nonabelian one. We show that there exist limits of the nonacyclic Reidemeister torsion at bifurcation points and the limits are expressed by using the derivation of the Alexander polynomial of the knot in this paper.

KW - Character varieties

KW - Knots

KW - Reidemeister torsion

KW - Twisted alexander invariant

UR - http://www.scopus.com/inward/record.url?scp=65249096284&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=65249096284&partnerID=8YFLogxK

U2 - 10.2140/agt.2007.7.1485

DO - 10.2140/agt.2007.7.1485

M3 - Article

AN - SCOPUS:65249096284

SN - 1472-2747

VL - 7

SP - 1485

EP - 1507

JO - Algebraic and Geometric Topology

JF - Algebraic and Geometric Topology

IS - 1

ER -

Limit values of the nonacyclic reidemeister torsion for knots

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this