Divisibility of twisted Alexander polynomials and fibered knots

Teruaki Kitano[1]; Takayuki Morifuji[2]

  • [1] Department of Mathematical and Computing Sciences Tokyo Institute of Technology 2-12-1-W8-43 Oh-okayama, Meguro-ku Tokyo 152-8552, Japan
  • [2] Department of Mathematics Tokyo University of Agriculture and Technology 2-24-16 Naka-cho, Koganei Tokyo 184-8588, Japan

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2005)

  • Volume: 4, Issue: 1, page 179-186
  • ISSN: 0391-173X

Abstract

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We prove that Wada’s twisted Alexander polynomial of a knot group associated to any nonabelian S L ( 2 , 𝔽 ) -representation is a polynomial. As a corollary, we show that it is always a monic polynomial of degree 4 g - 2 for a fibered knot of genus  g .

How to cite

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Kitano, Teruaki, and Morifuji, Takayuki. "Divisibility of twisted Alexander polynomials and fibered knots." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 4.1 (2005): 179-186. <http://eudml.org/doc/84553>.

@article{Kitano2005,
abstract = {We prove that Wada’s twisted Alexander polynomial of a knot group associated to any nonabelian $SL(2,\mathbb \{F\})$-representation is a polynomial. As a corollary, we show that it is always a monic polynomial of degree $4g-2$ for a fibered knot of genus $g$.},
affiliation = {Department of Mathematical and Computing Sciences Tokyo Institute of Technology 2-12-1-W8-43 Oh-okayama, Meguro-ku Tokyo 152-8552, Japan; Department of Mathematics Tokyo University of Agriculture and Technology 2-24-16 Naka-cho, Koganei Tokyo 184-8588, Japan},
author = {Kitano, Teruaki, Morifuji, Takayuki},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
language = {eng},
number = {1},
pages = {179-186},
publisher = {Scuola Normale Superiore, Pisa},
title = {Divisibility of twisted Alexander polynomials and fibered knots},
url = {http://eudml.org/doc/84553},
volume = {4},
year = {2005},
}

TY - JOUR
AU - Kitano, Teruaki
AU - Morifuji, Takayuki
TI - Divisibility of twisted Alexander polynomials and fibered knots
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 2005
PB - Scuola Normale Superiore, Pisa
VL - 4
IS - 1
SP - 179
EP - 186
AB - We prove that Wada’s twisted Alexander polynomial of a knot group associated to any nonabelian $SL(2,\mathbb {F})$-representation is a polynomial. As a corollary, we show that it is always a monic polynomial of degree $4g-2$ for a fibered knot of genus $g$.
LA - eng
UR - http://eudml.org/doc/84553
ER -

References

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