|
|||||
|
|
|
|
|
|
|
|
|
Displacing Lagrangian
toric fibers by extended probes
Miguel Abreu, Matthew Strom Borman and Dusa McDuff |
|
Algebraic & Geometric Topology 14 (2014) 687–752
|
Abstract |
|
In this paper we introduce a new way of displacing Lagrangian fibers in toric symplectic manifolds, a generalization of McDuff’s original method of probes. Extended probes are formed by deflecting one probe by another auxiliary probe. Using them, we are able to displace all fibers in Hirzebruch surfaces except those already known to be nondisplaceable, and can also displace an open dense set of fibers in the weighted projective space after resolving the singularities. We also investigate the displaceability question in sectors and their resolutions. There are still many cases in which there is an open set of fibers whose displaceability status is unknown. |
Keywords
symplectic manifolds, Lagrangian tori, nondisplaceable,
toric manifolds
|
Mathematical Subject Classification 2010
Primary: 53D12
Secondary: 14M25, 53D40
|
References |
Publication
Received: 29 May 2012
Accepted: 28 August 2013
Published: 30 January 2014
|
Authors |
| Miguel Abreu | |
| Centro de Análise Mathemática,
Geometria e Sistemas Dinâmicos Departamento de Mathemática Instituto Superior Técnico 1049-001 Lisboa Portugal |
|
| Matthew Strom Borman | |
| Department of Mathematics University of Chicago Chicago, IL 60637 USA |
|
| Dusa McDuff | |
| Mathematics Department Barnard College and Columbia University New York, NY 10027 USA |
|
|
