The Reidemeister-Turaev torsion of standard Spin c structures on Seifert fibered 3-manifolds
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 21 (2012) no. 4, pp. 745-768.

La torsion de Reidemeister-Turaev est un invariant des 3-variétés avec structure Spin c . Ici, une structure Spin c 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 c 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 c standard sur une variété de Seifert. La technique utilisée pour calculer la torsion est celle des diagrammes de Heegaard percés.

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.

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     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},
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     publisher = {Universit\'e Paul Sabatier, Institut de math\'ematiques},
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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, Série 6, Tome 21 (2012) no. 4, pp. 745-768. doi : 10.5802/afst.1349. http://archive.numdam.org/articles/10.5802/afst.1349/

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