東華大學圖書館 |

語系: 繁體中文

說明(常見問題)

回圖書館首頁

手機版館藏查詢

登入

回首頁

切換: 標籤 | MARC模式 | ISBD

Symplectic quasi-states and Lagrangi...

Borman, Matthew Strom.

FindBook

Google Book

Amazon

博客來

Symplectic quasi-states and Lagrangian topology.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Symplectic quasi-states and Lagrangian topology./
作者:	Borman, Matthew Strom.
面頁冊數:	173 p.
附註:	Source: Dissertation Abstracts International, Volume: 75-01(E), Section: B.
Contained By:	Dissertation Abstracts International75-01B(E).
標題:	Mathematics. -
電子資源:	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.
LDR:02205nmm a2200289 4500 001 1932251
005 20140805082245.5
008 140827s2013 ||||||||||||||||| ||eng d
020 $a 9781303422393
035 $a (MiAaPQ)AAI3595889
035 $a AAI3595889
040 $a MiAaPQ $c MiAaPQ
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
690 $a 0405
690 $a 0364
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