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

Yoshikazu Yamaguchi[1]

  • [1] University of Tokyo Graduate School of Mathematical Sciences 3-8-1 Komaba Meguro Tokyo 153-8914 (Japan)

Annales de l’institut Fourier (2008)

  • Volume: 58, Issue: 1, page 337-362
  • ISSN: 0373-0956

Abstract

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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 , ℂ ) -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.

How to cite

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Yamaguchi, Yoshikazu. "A relationship between the non-acyclic Reidemeister torsion and a zero of the acyclic Reidemeister torsion." Annales de l’institut Fourier 58.1 (2008): 337-362. <http://eudml.org/doc/10314>.

@article{Yamaguchi2008,
abstract = {We show a relationship between the non-acyclic Reidemeister torsion and a zero of the acyclic Reidemeister torsion for a $\lambda $-regular $\{\rm SU\}(2)$ or $\{\rm SL\}(2, \mathbb\{C\})$-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 $\{\rm SU\}(2)$-representations of its knot group.},
affiliation = {University of Tokyo Graduate School of Mathematical Sciences 3-8-1 Komaba Meguro Tokyo 153-8914 (Japan)},
author = {Yamaguchi, Yoshikazu},
journal = {Annales de l’institut Fourier},
keywords = {Reidemeister torsion; twisted Alexander invariant; knots; representation spaces},
language = {eng},
number = {1},
pages = {337-362},
publisher = {Association des Annales de l’institut Fourier},
title = {A relationship between the non-acyclic Reidemeister torsion and a zero of the acyclic Reidemeister torsion},
url = {http://eudml.org/doc/10314},
volume = {58},
year = {2008},
}

TY - JOUR
AU - Yamaguchi, Yoshikazu
TI - A relationship between the non-acyclic Reidemeister torsion and a zero of the acyclic Reidemeister torsion
JO - Annales de l’institut Fourier
PY - 2008
PB - Association des Annales de l’institut Fourier
VL - 58
IS - 1
SP - 337
EP - 362
AB - We show a relationship between the non-acyclic Reidemeister torsion and a zero of the acyclic Reidemeister torsion for a $\lambda $-regular ${\rm SU}(2)$ or ${\rm SL}(2, \mathbb{C})$-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 ${\rm SU}(2)$-representations of its knot group.
LA - eng
KW - Reidemeister torsion; twisted Alexander invariant; knots; representation spaces
UR - http://eudml.org/doc/10314
ER -

References

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