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Properties of Hamiltonian Torus Acti...

Fanoe, Andrew.

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Properties of Hamiltonian Torus Actions on Closed Symplectic Manifolds.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Properties of Hamiltonian Torus Actions on Closed Symplectic Manifolds./
Author:	Fanoe, Andrew.
Description:	97 p.
Notes:	Source: Dissertation Abstracts International, Volume: 74-09(E), Section: B.
Contained By:	Dissertation Abstracts International74-09B(E).
Subject:	Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3560818
ISBN:	9781303074325

Properties of Hamiltonian Torus Actions on Closed Symplectic Manifolds.
Fanoe, Andrew.

Properties of Hamiltonian Torus Actions on Closed Symplectic Manifolds. - 97 p.

Source: Dissertation Abstracts International, Volume: 74-09(E), Section: B.

Thesis (Ph.D.)--Columbia University, 2013.

In this thesis, we will study the properties of certain Hamiltonian torus actions on closed symplectic manifolds.

ISBN: 9781303074325Subjects--Topical Terms:

515831
Mathematics.

Properties of Hamiltonian Torus Actions on Closed Symplectic Manifolds.
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020 $a 9781303074325
035 $a (MiAaPQ)AAI3560818
035 $a AAI3560818
040 $a MiAaPQ $c MiAaPQ
100 1 $a Fanoe, Andrew. $3 2101192
245 1 0 $a Properties of Hamiltonian Torus Actions on Closed Symplectic Manifolds.
300 $a 97 p.
500 $a Source: Dissertation Abstracts International, Volume: 74-09(E), Section: B.
500 $a Adviser: Dusa McDuff.
502 $a Thesis (Ph.D.)--Columbia University, 2013.
520 $a In this thesis, we will study the properties of certain Hamiltonian torus actions on closed symplectic manifolds.
520 $a First, we will consider counting Hamiltonian torus actions on closed, symplectic manifolds M with 2-dimensional second cohomology. In particular, all such manifolds are bundles with fiber and base equal to projective spaces. We use cohomological techniques to show that there is a unique toric structure if the fiber has a smaller dimension than the base. Furthermore, if the fiber and base are both at least 2-dimensional projective spaces, we show that there is a finite number of toric structures on M that are compatible with some symplectic structure on M. Additionally, we show there is uniqueness in certain other cases, such as the case where M is a monotone symplectic manifold.
520 $a Finally, we will be interested in the existence of symplectic, non-Hamiltonian circle actions on closed symplectic 6-manifolds. In particular, we will use J-holomorphic curve techniques to show that there are no such actions that satisfy certain fixed point conditions. This lends support to the conjecture that there are no such actions with a non-empty set of isolated fixed points.
590 $a School code: 0054.
650 4 $a Mathematics. $3 515831
650 4 $a Theoretical Mathematics. $3 1672766
690 $a 0405
690 $a 0642
710 2 $a Columbia University. $b Mathematics. $3 1684292
773 0 $t Dissertation Abstracts International $g 74-09B(E).
790 $a 0054
791 $a Ph.D.
792 $a 2013
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3560818