A spectral viewpoint of the linking form in the 3-torus

Adrien Boulanger (1, 2)

1 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche
2 IRMAR - Institut de Recherche Mathématique de Rennes

We compute the linking number between any two collections of homologically trivial oriented geodesics of the three torus endowed with the flat metric. As a corollary we find a new formula for the linking number of such collection of geodesics which comes from the geodesic flow of the two flat torus $\mathbb{T}^2$. Our method relies on spectral theory of differential forms and on the linking form of T. Vogel.

Domaines: Topologie géométrique [math.GT]; Géométrie différentielle [math.DG]; Théorie spectrale [math.SP]

Adrien Boulanger. A spectral viewpoint of the linking form in the 3-torus. 2017. ⟨hal-01612291⟩