Tropical constructions of algebraic knots in the 3-dimensional real projective space
type: Dataset
description: 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.
identifier: NNT: 2012STRAD030
issued: 2026-06-01T05:24:49.294034
language: en
modified: 2026-06-01T05:24:49.294042
contact point: Organization
  fn: CCSD
keyword: courbe-algebrique-reelle
keyword: courbe-tropicale
keyword: courbe-tropicale-reelle
keyword: entrelacs
keyword: infoeu-reposemanticsdoctoralthesis
keyword: knot
keyword: link
keyword: mathmath-atmathematics-mathalgebraic-topology-mathat
keyword: noeud
keyword: patchwork
keyword: real-algebraic-curve
keyword: real-tropical-curve
keyword: theses
keyword: tropical-curve
landing page: https://theses.hal.science/tel-00733721

Tropical constructions of algebraic knots in the 3-dimensional real projective space
type: Distribution
format: HTML
issued: 2026-06-01T05:24:49.454770
modified: 2026-06-01T05:24:49.249588
access URL: https://theses.hal.science/tel-00733721

test_moissonnage_selune
type: Agent