Vol. 307, No. 2, 2020

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A spectral approach to the linking number in the 3-torus

Adrien Boulanger

Vol. 307 (2020), No. 2, 257–281
Abstract

Given a closed Riemannian manifold and a pair of multicurves in it, we give a formula relating the linking number of the latter to the spectral theory of the Laplace operator acting on differential 1-forms. As an application, we compute the linking number of any two multigeodesics of the flat torus of dimension 3, generalising a result of P. Dehornoy.

Keywords
linking number, spectral theory, differential geometry
Mathematical Subject Classification 2010
Primary: 55M99, 58J35, 58J50
Milestones
Received: 4 February 2019
Revised: 5 February 2020
Accepted: 30 April 2020
Published: 4 September 2020
Authors
Adrien Boulanger
Institut mathématique de Marseille
France