The Reidemeister-Turaev torsion of standard Spin c structures on Seifert fibered 3-manifolds

Yuya Koda[1]

  • [1] Mathematical Institute, Tohoku University, Sendai, 980-8578, Japan

Annales de la faculté des sciences de Toulouse Mathématiques (2012)

  • Volume: 21, Issue: 4, page 745-768
  • ISSN: 0240-2963

Abstract

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The Reidemeister-Turaev torsion is an invariant of 3-manifolds equipped with Spin c structures. Here, a Spin c structure of a 3-manifold is a homology class of non-singular vector fields on it. Each Seifert fibered 3-manifold has a standard Spin c structure, which is represented as a non-singular vector field the set of whose orbits give a Seifert fibration. We provide an algorithm for computing the Reidemeister-Turaev torsion of the standard Spin c structure on a Seifert fibered 3-manifold. The machinery used to compute the torsion is that of punctured Heegaard diagrams.

How to cite

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Koda, Yuya. "The Reidemeister-Turaev torsion of standard Spin$^c$ structures on Seifert fibered 3-manifolds." Annales de la faculté des sciences de Toulouse Mathématiques 21.4 (2012): 745-768. <http://eudml.org/doc/250991>.

@article{Koda2012,
abstract = {The Reidemeister-Turaev torsion is an invariant of 3-manifolds equipped with Spin$^c$ structures. Here, a Spin$^c$ structure of a 3-manifold is a homology class of non-singular vector fields on it. Each Seifert fibered 3-manifold has a standard Spin$^c$ structure, which is represented as a non-singular vector field the set of whose orbits give a Seifert fibration. We provide an algorithm for computing the Reidemeister-Turaev torsion of the standard Spin$^c$ structure on a Seifert fibered 3-manifold. The machinery used to compute the torsion is that of punctured Heegaard diagrams.},
affiliation = {Mathematical Institute, Tohoku University, Sendai, 980-8578, Japan},
author = {Koda, Yuya},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
keywords = {Reidemeister torsion; Reidemeister-Turaev torsion; Seifert 3-manifolds.},
language = {eng},
month = {10},
number = {4},
pages = {745-768},
publisher = {Université Paul Sabatier, Toulouse},
title = {The Reidemeister-Turaev torsion of standard Spin$^c$ structures on Seifert fibered 3-manifolds},
url = {http://eudml.org/doc/250991},
volume = {21},
year = {2012},
}

TY - JOUR
AU - Koda, Yuya
TI - The Reidemeister-Turaev torsion of standard Spin$^c$ structures on Seifert fibered 3-manifolds
JO - Annales de la faculté des sciences de Toulouse Mathématiques
DA - 2012/10//
PB - Université Paul Sabatier, Toulouse
VL - 21
IS - 4
SP - 745
EP - 768
AB - The Reidemeister-Turaev torsion is an invariant of 3-manifolds equipped with Spin$^c$ structures. Here, a Spin$^c$ structure of a 3-manifold is a homology class of non-singular vector fields on it. Each Seifert fibered 3-manifold has a standard Spin$^c$ structure, which is represented as a non-singular vector field the set of whose orbits give a Seifert fibration. We provide an algorithm for computing the Reidemeister-Turaev torsion of the standard Spin$^c$ structure on a Seifert fibered 3-manifold. The machinery used to compute the torsion is that of punctured Heegaard diagrams.
LA - eng
KW - Reidemeister torsion; Reidemeister-Turaev torsion; Seifert 3-manifolds.
UR - http://eudml.org/doc/250991
ER -

References

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