An introduction to the abelian Reidemeister torsion of three-dimensional manifolds

Massuyeau, Gwénaël

Annales mathématiques Blaise Pascal, Tome 18 (2011) no. 1, pp. 61-140.

Ces notes accompagnent un mini-cours donné à l’école d’automne “Tresses in Pau” en Octobre 2009. Nous introduisons la torsion de Reidemeister des variétés de dimension $3$ et ses raffinements par Turaev. Nous survolons quelques applications, et notamment les relations qu’entretient la torsion de Reidemeister avec d’autres invariants classiques.

These notes accompany some lectures given at the autumn school “Tresses in Pau” in October 2009. The abelian Reidemeister torsion for $3$-manifolds, and its refinements by Turaev, are introduced. Some applications, including relations between the Reidemeister torsion and other classical invariants, are surveyed.

Classification : 57M27, 57N10, 57M05, 57M10
Keywords: $3$-manifold, Reidemeister torsion, Alexander polynomial
Mot clés : variété de dimension $3$, torsion de Reidemeister, pôlynome d’Alexander

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