Lagrangian tori in \(\mathbb{R}^ 4\)
type: Item
instance of: scholarly article
title: Lagrangian tori in \(\mathbb{R}^ 4\)
zbMATH Open document ID: 0861.53029
author: Karl Murad Luttinger
published in: Journal of Differential Geometry
publication date: 1996-07-29T00:00:00Z
review text: One of the problems in symplectic topology is the question of whether or not any Lagrangian tori are topologically knotted. The author shows that a large number of isotopy classes of embeddings of the torus in 4-space do not contain Lagrangian representatives. It is also shown that a countable number of symplectic Dehn surgeries can be performed on any Lagrangian torus. The topological obstructions to a Lagrangian embedding are formulated in the language of classical knot theory. As examples he studies the torus spin knots and proves that there is no nontrivial torus spin knot admitting a Lagrangian realization in \((\mathbb{R}^4,\omega)\).
Mathematics Subject Classification ID: 53C15
Mathematics Subject Classification ID: 57R40
Mathematics Subject Classification ID: 37J99
Mathematics Subject Classification ID: 57R15
Mathematics Subject Classification ID: 57R52
Mathematics Subject Classification ID: 57R65
zbMATH DE Number: 894383
zbMATH Keywords: surgery
zbMATH Keywords: torus knots
zbMATH Keywords: symplectic topology
zbMATH Keywords: Lagrangian tori
zbMATH Keywords: Lagrangian embedding
zbMATH Keywords: knot theory
reviewed by: Stanisław Janeczko
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4310/jdg/1214457232
OpenAlex ID: W1515555836
Wikidata QID: Q115177939
DOI: 10.4310/JDG/1214457232
description: scientific article; zbMATH DE number 894383