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This article is available for purchase or by subscription. See below.
Abstract
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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.
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Keywords
linking number, spectral theory, differential geometry
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Mathematical Subject Classification 2010
Primary: 55M99, 58J35, 58J50
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Milestones
Received: 4 February 2019
Revised: 5 February 2020
Accepted: 30 April 2020
Published: 4 September 2020
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