Tropical constructions of algebraic knots in the 3-dimensional real projective space

In this thesis, we construct real tropical curves in R^3 whose projectivization - which is a projective link in RP^3 - has 2connected components, one of them being isotopic to a given knot. For some torus knots, it is possible to modify thetropical construction such that the corresponding projective link is a knot (with a single component) isotopic to the giventorus knot. For each of these real tropical curve, we use a recent result of G. Mikhalkin, asserting the existence of a realnon singular algebraic curve in RP^3, of the same genus and degree as the real tropical curve, and isotopic to thecorresponding projective link.

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Source https://theses.hal.science/tel-00733721
Author Will, Etienne
Maintainer CCSD
Last Updated June 1, 2026, 05:24 (UTC)
Created June 1, 2026, 05:24 (UTC)
Identifier NNT: 2012STRAD030
Language en
Rights https://about.hal.science/hal-authorisation-v1/
contributor Institut de Recherche Mathématique Avancée (IRMA) ; Université de Strasbourg (UNISTRA)-Centre National de la Recherche Scientifique (CNRS)
creator Will, Etienne
date 2012-09-20T00:00:00
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harvest_source_id 3374d638-d20b-4672-ba96-a23232d55657
harvest_source_title test moissonnage SELUNE
metadata_modified 2026-03-30T00:00:00
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