Home > Research > Publications & Outputs > Unlinking and unknottedness of monotone Lagrang...

Research

Associated organisational unit

Electronic data

  • 1211.6633

    Submitted manuscript, 573 KB, PDF document

    Available under license: CC BY-NC: Creative Commons Attribution-NonCommercial 4.0 International License

Links

Text available via DOI:

Keywords

View graph of relations

Unlinking and unknottedness of monotone Lagrangian submanifolds

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Published

Standard

Unlinking and unknottedness of monotone Lagrangian submanifolds. / Dimitroglou Rizell, Georgios; Evans, Jonathan David.
In: Geometry and Topology, Vol. 18, No. 2, 07.04.2014, p. 997-1034.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Dimitroglou Rizell, G & Evans, JD 2014, 'Unlinking and unknottedness of monotone Lagrangian submanifolds', Geometry and Topology, vol. 18, no. 2, pp. 997-1034. https://doi.org/10.2140/gt.2014.18.997

APA

Dimitroglou Rizell, G., & Evans, J. D. (2014). Unlinking and unknottedness of monotone Lagrangian submanifolds. Geometry and Topology, 18(2), 997-1034. https://doi.org/10.2140/gt.2014.18.997

Vancouver

Dimitroglou Rizell G, Evans JD. Unlinking and unknottedness of monotone Lagrangian submanifolds. Geometry and Topology. 2014 Apr 7;18(2):997-1034. doi: 10.2140/gt.2014.18.997

Author

Dimitroglou Rizell, Georgios ; Evans, Jonathan David. / Unlinking and unknottedness of monotone Lagrangian submanifolds. In: Geometry and Topology. 2014 ; Vol. 18, No. 2. pp. 997-1034.

Bibtex

@article{89337d69100c4f00ace532fdf4953e73,
title = "Unlinking and unknottedness of monotone Lagrangian submanifolds",
abstract = " Under certain topological assumptions, we show that two monotone Lagrangian submanifolds embedded in the standard symplectic vector space with the same monotonicity constant cannot link one another and that, individually, their smooth knot type is determined entirely by the homotopy theoretic data which classifies the underlying Lagrangian immersion. The topological assumptions are satisfied by a large class of manifolds which are realised as monotone Lagrangians, including tori. After some additional homotopy theoretic calculations, we deduce that all monotone Lagrangian tori in the symplectic vector space of odd complex dimension at least five are smoothly isotopic. ",
keywords = "Lagrangian submanifold, symplectic manifold, monotone, torus, knot",
author = "{Dimitroglou Rizell}, Georgios and Evans, {Jonathan David}",
year = "2014",
month = apr,
day = "7",
doi = "10.2140/gt.2014.18.997",
language = "English",
volume = "18",
pages = "997--1034",
journal = "Geometry and Topology",
issn = "1364-0380",
publisher = "Mathematical Sciences Publishers",
number = "2",

}

RIS

TY - JOUR

T1 - Unlinking and unknottedness of monotone Lagrangian submanifolds

AU - Dimitroglou Rizell, Georgios

AU - Evans, Jonathan David

PY - 2014/4/7

Y1 - 2014/4/7

N2 - Under certain topological assumptions, we show that two monotone Lagrangian submanifolds embedded in the standard symplectic vector space with the same monotonicity constant cannot link one another and that, individually, their smooth knot type is determined entirely by the homotopy theoretic data which classifies the underlying Lagrangian immersion. The topological assumptions are satisfied by a large class of manifolds which are realised as monotone Lagrangians, including tori. After some additional homotopy theoretic calculations, we deduce that all monotone Lagrangian tori in the symplectic vector space of odd complex dimension at least five are smoothly isotopic.

AB - Under certain topological assumptions, we show that two monotone Lagrangian submanifolds embedded in the standard symplectic vector space with the same monotonicity constant cannot link one another and that, individually, their smooth knot type is determined entirely by the homotopy theoretic data which classifies the underlying Lagrangian immersion. The topological assumptions are satisfied by a large class of manifolds which are realised as monotone Lagrangians, including tori. After some additional homotopy theoretic calculations, we deduce that all monotone Lagrangian tori in the symplectic vector space of odd complex dimension at least five are smoothly isotopic.

KW - Lagrangian submanifold

KW - symplectic manifold

KW - monotone

KW - torus

KW - knot

U2 - 10.2140/gt.2014.18.997

DO - 10.2140/gt.2014.18.997

M3 - Journal article

VL - 18

SP - 997

EP - 1034

JO - Geometry and Topology

JF - Geometry and Topology

SN - 1364-0380

IS - 2

ER -