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Symplectic quasi-states and Lagrangi...

Borman, Matthew Strom.

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Symplectic quasi-states and Lagrangian topology.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Symplectic quasi-states and Lagrangian topology./
Author:	Borman, Matthew Strom.
Description:	173 p.
Notes:	Source: Dissertation Abstracts International, Volume: 75-01(E), Section: B.
Contained By:	Dissertation Abstracts International75-01B(E).
Subject:	Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3595889
ISBN:	9781303422393

Symplectic quasi-states and Lagrangian topology.
Borman, Matthew Strom.

Symplectic quasi-states and Lagrangian topology. - 173 p.

Source: Dissertation Abstracts International, Volume: 75-01(E), Section: B.

Thesis (Ph.D.)--The University of Chicago, 2013.

In the first part of this thesis we develop a geometric method for building new symplectic quasi-states from known symplectic quasi-states using symplectic reduction. Combined with a construction due to Abreu and Macarini, in each dimension at least four we produce a closed symplectic toric manifold with a continuum of disjoint non-displaceable Lagrangian tori each super-heavy for a distinct symplectic quasi-states. By using McDuff's method of probes, we also show how Ostrover and Tyomkin's method for finding distinct spectral quasi-states in symplectic toric Fano manifolds can also be used to find different superheavy toric fibers.

ISBN: 9781303422393Subjects--Topical Terms:

515831
Mathematics.

Symplectic quasi-states and Lagrangian topology.
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100 1 $a Borman, Matthew Strom. $3 2049881
245 1 0 $a Symplectic quasi-states and Lagrangian topology.
300 $a 173 p.
500 $a Source: Dissertation Abstracts International, Volume: 75-01(E), Section: B.
500 $a Adviser: Leonid Polterovich.
502 $a Thesis (Ph.D.)--The University of Chicago, 2013.
520 $a In the first part of this thesis we develop a geometric method for building new symplectic quasi-states from known symplectic quasi-states using symplectic reduction. Combined with a construction due to Abreu and Macarini, in each dimension at least four we produce a closed symplectic toric manifold with a continuum of disjoint non-displaceable Lagrangian tori each super-heavy for a distinct symplectic quasi-states. By using McDuff's method of probes, we also show how Ostrover and Tyomkin's method for finding distinct spectral quasi-states in symplectic toric Fano manifolds can also be used to find different superheavy toric fibers.
520 $a In the second part of this thesis 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 non-displaceable, 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.
590 $a School code: 0330.
650 4 $a Mathematics. $3 515831
650 4 $a Applied Mathematics. $3 1669109
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710 2 $a The University of Chicago. $b Mathematics. $3 2049825
773 0 $t Dissertation Abstracts International $g 75-01B(E).
790 $a 0330
791 $a Ph.D.
792 $a 2013
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3595889