Non abelian Reidemeister torsion and volume form on the SU(2)-representation space of knot groups

Jérôme Dubois[1]

  • [1] Université de Genève, section de mathématiques, CP64, 2-4 rue du lièvre, 1211 Genève 4 (Suisse), Université Blaise Pascal, laboratoire de mathématiques, avenue des Landais, 63177 Aubière cedex (France)

Annales de l’institut Fourier (2005)

  • Volume: 55, Issue: 5, page 1685-1734
  • ISSN: 0373-0956

Abstract

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For a knot K in the 3-sphere and a regular representation of its group G K into SU(2) we construct a non abelian Reidemeister torsion form on the first twisted cohomology group of the knot exterior. This non abelian Reidemeister torsion form provides a volume form on the SU(2)-representation space of G K . In another way, we construct using Casson’s original construction a natural volume form on the SU(2)-representation space of G K . Next, we compare these two apparently different points of view on the representation variety and finally prove that they produce the same topological knot.

How to cite

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Dubois, Jérôme. "Non abelian Reidemeister torsion and volume form on the SU(2)-representation space of knot groups." Annales de l’institut Fourier 55.5 (2005): 1685-1734. <http://eudml.org/doc/116229>.

@article{Dubois2005,
abstract = {For a knot $K$ in the 3-sphere and a regular representation of its group $G_K$ into SU(2) we construct a non abelian Reidemeister torsion form on the first twisted cohomology group of the knot exterior. This non abelian Reidemeister torsion form provides a volume form on the SU(2)-representation space of $G_K$. In another way, we construct using Casson’s original construction a natural volume form on the SU(2)-representation space of $G_K$. Next, we compare these two apparently different points of view on the representation variety and finally prove that they produce the same topological knot.},
affiliation = {Université de Genève, section de mathématiques, CP64, 2-4 rue du lièvre, 1211 Genève 4 (Suisse), Université Blaise Pascal, laboratoire de mathématiques, avenue des Landais, 63177 Aubière cedex (France)},
author = {Dubois, Jérôme},
journal = {Annales de l’institut Fourier},
keywords = {Knot groups; representation space; volume form; Reidemeister torsion; Casson invariant; adjoint representation; SU(2); SU(2)-representation; knot group},
language = {eng},
number = {5},
pages = {1685-1734},
publisher = {Association des Annales de l'Institut Fourier},
title = {Non abelian Reidemeister torsion and volume form on the SU(2)-representation space of knot groups},
url = {http://eudml.org/doc/116229},
volume = {55},
year = {2005},
}

TY - JOUR
AU - Dubois, Jérôme
TI - Non abelian Reidemeister torsion and volume form on the SU(2)-representation space of knot groups
JO - Annales de l’institut Fourier
PY - 2005
PB - Association des Annales de l'Institut Fourier
VL - 55
IS - 5
SP - 1685
EP - 1734
AB - For a knot $K$ in the 3-sphere and a regular representation of its group $G_K$ into SU(2) we construct a non abelian Reidemeister torsion form on the first twisted cohomology group of the knot exterior. This non abelian Reidemeister torsion form provides a volume form on the SU(2)-representation space of $G_K$. In another way, we construct using Casson’s original construction a natural volume form on the SU(2)-representation space of $G_K$. Next, we compare these two apparently different points of view on the representation variety and finally prove that they produce the same topological knot.
LA - eng
KW - Knot groups; representation space; volume form; Reidemeister torsion; Casson invariant; adjoint representation; SU(2); SU(2)-representation; knot group
UR - http://eudml.org/doc/116229
ER -

References

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