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arXiv:1203.1074

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Title: Displacing Lagrangian toric fibers by extended probes
Authors: Miguel Abreu, Matthew Strom Borman, Dusa McDuff
Categories: math.SG Symplectic Geometry
Comments: 53 pages, 26 figures; v3: minor corrections and updated references. To appear in Algebraic & Geometric Topology
MSC: 53D12, 14M25, 53D40
Journal reference: Algebr. Geom. Topol. 14(2):687-752, 2014 (DOI 10.2140/agt.2014.14.687)

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 P(1,3,5) 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.

Owner: Matthew Strom Borman
Version 1: Mon, 5 Mar 2012 23:37:36 GMT
Version 2: Tue, 29 May 2012 19:36:47 GMT
Version 3: Mon, 2 Sep 2013 02:58:58 GMT

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