The Reidemeister-Turaev torsion is an invariant of 3-manifolds equipped with Spin structures. Here, a Spin 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 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 structure on a Seifert fibered 3-manifold. The machinery used to compute the torsion is that of punctured Heegaard diagrams.
La torsion de Reidemeister-Turaev est un invariant des 3-variétés avec structure Spin. Ici, une structure Spin d’une 3-variété est une classe d’homologie de champ de vecteurs sans singularités sur elle. Chaque variété de Seifert a une structure Spin standard, qui est représentée comme un champ de vecteurs sans singularités dont l’ensemble des orbites donne une fibration de Seifert. Nous fournissons un algorithme pour calculer la torsion de Reidemeister-Turaev de la structure Spin standard sur une variété de Seifert. La technique utilisée pour calculer la torsion est celle des diagrammes de Heegaard percés.
@article{AFST_2012_6_21_4_745_0,
author = {Yuya Koda},
title = {The {Reidemeister-Turaev} torsion of standard {Spin}$^c$ structures on {Seifert} fibered 3-manifolds},
journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
pages = {745--768},
publisher = {Universit\'e Paul Sabatier, Institut de Math\'ematiques},
address = {Toulouse},
volume = {Ser. 6, 21},
number = {4},
year = {2012},
doi = {10.5802/afst.1349},
mrnumber = {3052029},
zbl = {1255.57022},
language = {en},
url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1349/}
}
TY - JOUR AU - Yuya Koda 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 PY - 2012 SP - 745 EP - 768 VL - 21 IS - 4 PB - Université Paul Sabatier, Institut de Mathématiques PP - Toulouse UR - https://afst.centre-mersenne.org/articles/10.5802/afst.1349/ DO - 10.5802/afst.1349 LA - en ID - AFST_2012_6_21_4_745_0 ER -
%0 Journal Article %A Yuya Koda %T The Reidemeister-Turaev torsion of standard Spin$^c$ structures on Seifert fibered 3-manifolds %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2012 %P 745-768 %V 21 %N 4 %I Université Paul Sabatier, Institut de Mathématiques %C Toulouse %U https://afst.centre-mersenne.org/articles/10.5802/afst.1349/ %R 10.5802/afst.1349 %G en %F AFST_2012_6_21_4_745_0
Yuya Koda. The Reidemeister-Turaev torsion of standard Spin$^c$ structures on Seifert fibered 3-manifolds. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 21 (2012) no. 4, pp. 745-768. doi : 10.5802/afst.1349. https://afst.centre-mersenne.org/articles/10.5802/afst.1349/
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