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Bi-invariant norms on the group of s...

State University of New York at Stony Brook.

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Bi-invariant norms on the group of symplectomorphisms.

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Bi-invariant norms on the group of symplectomorphisms./
作者:	Han, Zhigang.
面頁冊數:	64 p.
附註:	Adviser: Dusa McDuff.
Contained By:	Dissertation Abstracts International68-01B.
標題:	Mathematics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3246833

Bi-invariant norms on the group of symplectomorphisms.
Han, Zhigang.

Bi-invariant norms on the group of symplectomorphisms. - 64 p.

Adviser: Dusa McDuff.

Thesis (Ph.D.)--State University of New York at Stony Brook, 2006.

The group of diffeomorphisms of a symplectic manifold (M, o) preserving the symplectic form is called the symplectomorphism group of (M, o) and denoted by Symp(M, o). It has a very important subgroup Ham( M, o) called the Hamiltonian diffeomorphism group. The group Ham(M, o) admits a natural bi-invariant norm, known as the Hofer norm. In this thesis we study several aspects of bi-invariant norms on Symp(M, o), including the bounded isometry conjecture of Lalonde and Polterovich. In particular, we prove the conjecture for the Kodaira-Thurston manifold and for the 4-torus with all linear symplectic forms. Relatedly, we observe that there is an obstruction to extending the Hofer norm bi-invariantly to the identity component Symp0( M, o) of Symp(M, o). This obstruction is shown to be non-trivial in some cases. We also prove that no Finsler norm on Ham( T2n , o) satisfying a strong form of the invariance condition can extend to a bi-invariant norm on Symp0( T2n , o). Other bi-invariant norms on Symp0(M, o) are studied as well and the induced topologies are discussed.Subjects--Topical Terms:

515831
Mathematics.

Bi-invariant norms on the group of symplectomorphisms.
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100 1 $a Han, Zhigang. $3 1019418
245 1 0 $a Bi-invariant norms on the group of symplectomorphisms.
300 $a 64 p.
500 $a Adviser: Dusa McDuff.
500 $a Source: Dissertation Abstracts International, Volume: 68-01, Section: B, page: 0326.
502 $a Thesis (Ph.D.)--State University of New York at Stony Brook, 2006.
520 $a The group of diffeomorphisms of a symplectic manifold (M, o) preserving the symplectic form is called the symplectomorphism group of (M, o) and denoted by Symp(M, o). It has a very important subgroup Ham( M, o) called the Hamiltonian diffeomorphism group. The group Ham(M, o) admits a natural bi-invariant norm, known as the Hofer norm. In this thesis we study several aspects of bi-invariant norms on Symp(M, o), including the bounded isometry conjecture of Lalonde and Polterovich. In particular, we prove the conjecture for the Kodaira-Thurston manifold and for the 4-torus with all linear symplectic forms. Relatedly, we observe that there is an obstruction to extending the Hofer norm bi-invariantly to the identity component Symp0( M, o) of Symp(M, o). This obstruction is shown to be non-trivial in some cases. We also prove that no Finsler norm on Ham( T2n , o) satisfying a strong form of the invariance condition can extend to a bi-invariant norm on Symp0( T2n , o). Other bi-invariant norms on Symp0(M, o) are studied as well and the induced topologies are discussed.
590 $a School code: 0771.
650 4 $a Mathematics. $3 515831
690 $a 0405
710 2 $a State University of New York at Stony Brook. $3 1019194
773 0 $t Dissertation Abstracts International $g 68-01B.
790 $a 0771
790 1 0 $a McDuff, Dusa, $e advisor
791 $a Ph.D.
792 $a 2006
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3246833