The Reidemeister-Turaev torsion of standard Spin${}^c$ structures on Seifert fibered 3-manifolds

Koda, Yuya

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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