Nonstandard Lagrangian tori and pseudotoric structures
type: Item
instance of: scholarly article
title: Nonstandard Lagrangian tori and pseudotoric structures
zbMATH Open document ID: 1284.14072
author: N. A. Tyurin
published in: Theoretical and Mathematical Physics
publication date: 2014-01-30T00:00:00Z
review text: An important mathematical problem is the classification of Lagrangian tori or, more generally, of all possible Lagrangian submanifolds in symplectic manifolds up to a symplectomorphism or Hamiltonian isotopy. In the present paper, the author investigates twisted tori [\textit{Y. Chekanov} and \textit{F. Schlenk}, Electron. Res. Announc. Math. Sci. 17, 104--121 (2010; Zbl 1201.53083)], which are examples of exotic monotonic tori. The author shows that exotic Lagrangian tori constructed by Chekanov and Schlenk can be obtained for a large class of toric manifolds. For this, he translates their original construction into the language of pseudotoric structures. At the end of the paper, the author constructs, as an example, exotic Lagrangian tori on a del Pezzo surface of degree six, as an answer to the problem posed in [loc. cit.] of constructing nonstandard tori in \(\mathbb {CP}^2_3\) (the projective plane with three blown-up points).
reviewed by: Andreea Olteanu
Mathematics Subject Classification ID: 14M25
Mathematics Subject Classification ID: 53D05
zbMATH DE Number: 6252390
zbMATH Keywords: Lagrangian torus
zbMATH Keywords: exotic torus
zbMATH Keywords: Chekanov torus
zbMATH Keywords: pseudotoric structure
zbMATH Keywords: del Pezzo surface
MaRDI profile type: Publication
full work available at URL: s11232-012-0067-9
OpenAlex ID: W2023450405
cites work: Q4382057
cites work: Nontoric foliations by Lagrangian tori of toric Fano varieties
cites work: Pseudotoric Lagrangian fibrations of toric and nontoric Fano varieties
cites work: Chekanov tori and pseudotoric structures
cites work: The Poincaré-Lyapunov-Liouville-Arnol'd theorem
DOI: 10.1007/S11232-012-0067-9
description: scientific article