On the twisted Alexander polynomial for metabelian representations into SL2(C)

Yoshikazu Yamaguchi

doi:10.1016/j.topol.2013.07.006

On the twisted Alexander polynomial for metabelian representations into SL2(C)

Yoshikazu Yamaguchi^*

^*Corresponding author for this work

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

3 Citations (Scopus)

Abstract

We observe the twisted Alexander polynomial for metabelian representations of knot groups into SL2(C) and study relations to the characterizations of metabelian representations in the character varieties. We give a factorization of the twisted Alexander polynomial for irreducible metabelian representations with the adjoint action on sl2(C), in which the Alexander polynomial and the twisted Alexander polynomial appear as factors. We also show several explicit examples.

Original language	English
Pages (from-to)	1760-1772
Number of pages	13
Journal	Topology and its Applications
Volume	160
Issue number	13
DOIs	https://doi.org/10.1016/j.topol.2013.07.006
Publication status	Published - 2013 Aug 15
Externally published	Yes

Keywords

Binary dihedral representations
Knots
Metabelian representations
PriThe twisted Alexander polynomial
SL2(C)-representations

ASJC Scopus subject areas

Geometry and Topology

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10.1016/j.topol.2013.07.006

Cite this

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title = "On the twisted Alexander polynomial for metabelian representations into SL2(C)",

abstract = "We observe the twisted Alexander polynomial for metabelian representations of knot groups into SL2(C) and study relations to the characterizations of metabelian representations in the character varieties. We give a factorization of the twisted Alexander polynomial for irreducible metabelian representations with the adjoint action on sl2(C), in which the Alexander polynomial and the twisted Alexander polynomial appear as factors. We also show several explicit examples.",

keywords = "Binary dihedral representations, Knots, Metabelian representations, PriThe twisted Alexander polynomial, SL2(C)-representations",

author = "Yoshikazu Yamaguchi",

note = "Funding Information: This research was supported by Research Fellowships of the Japan Society for the Promotion of Science for Young Scientists. The author would like to express his thanks to Stephan Friedl for his useful comments at RIMS seminar “Twisted topological invariants and topology of low-dimensional manifolds”. The author wishes to express his thanks to Kunio Murasugi for his helpful comments and suggestions. The author also would like to express his gratitude to the referee for his or her careful reading and many comments to improve this paper.",

year = "2013",

month = aug,

day = "15",

doi = "10.1016/j.topol.2013.07.006",

language = "English",

volume = "160",

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journal = "Topology and its Applications",

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TY - JOUR

T1 - On the twisted Alexander polynomial for metabelian representations into SL2(C)

AU - Yamaguchi, Yoshikazu

N1 - Funding Information: This research was supported by Research Fellowships of the Japan Society for the Promotion of Science for Young Scientists. The author would like to express his thanks to Stephan Friedl for his useful comments at RIMS seminar “Twisted topological invariants and topology of low-dimensional manifolds”. The author wishes to express his thanks to Kunio Murasugi for his helpful comments and suggestions. The author also would like to express his gratitude to the referee for his or her careful reading and many comments to improve this paper.

PY - 2013/8/15

Y1 - 2013/8/15

N2 - We observe the twisted Alexander polynomial for metabelian representations of knot groups into SL2(C) and study relations to the characterizations of metabelian representations in the character varieties. We give a factorization of the twisted Alexander polynomial for irreducible metabelian representations with the adjoint action on sl2(C), in which the Alexander polynomial and the twisted Alexander polynomial appear as factors. We also show several explicit examples.

AB - We observe the twisted Alexander polynomial for metabelian representations of knot groups into SL2(C) and study relations to the characterizations of metabelian representations in the character varieties. We give a factorization of the twisted Alexander polynomial for irreducible metabelian representations with the adjoint action on sl2(C), in which the Alexander polynomial and the twisted Alexander polynomial appear as factors. We also show several explicit examples.

KW - Binary dihedral representations

KW - Knots

KW - Metabelian representations

KW - PriThe twisted Alexander polynomial

KW - SL2(C)-representations

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DO - 10.1016/j.topol.2013.07.006

M3 - Article

AN - SCOPUS:84882855822

VL - 160

SP - 1760

EP - 1772

JO - Topology and its Applications

JF - Topology and its Applications

SN - 0166-8641

IS - 13

ER -

On the twisted Alexander polynomial for metabelian representations into SL2(C)

Abstract

Keywords

ASJC Scopus subject areas

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