On the algebraic structure of relative hamiltonian diffeomorphism group

Download

index.pdf

Date

2008

Author

Demir, Ali Sait

Metadata

Show full item record

Item Usage Stats

39
views

18
downloads

Let M be smooth symplectic closed manifold and L a closed Lagrangian submanifold of M. It was shown by Ozan that Ham(M,L): the relative Hamiltonian diffeomorphisms on M fixing the Lagrangian submanifold L setwise is a subgroup which is equal to the kernel of the restriction of the flux homomorphism to the universal cover of the identity component of the relative symplectomorphisms. In this thesis we show that Ham(M,L) is a non-simple perfect group, by adopting a technique due to Thurston, Herman, and Banyaga. This technique requires the diffeomorphism group be transitive where this property fails to exist in our case.

Subject Keywords

Mathematics., Topology.

URI

http://etd.lib.metu.edu.tr/upload/12609301/index.pdf
https://hdl.handle.net/11511/17605

Collections

Graduate School of Natural and Applied Sciences, Thesis

Suggestions

OpenMETU
Core

Equivariant cross sections of complex Stiefel manifolds Onder, T (Elsevier BV, 2001-01-16) Let G be a finite group and let M be a unitary representation space of G. A solution to the existence problem of G-equivariant cross sections of the complex Stiefel manifold W-k(M) of unitary k-frames over the unit sphere S(M) is given under mild restrictions on G and on fixed point sets. In the case G is an even ordered group, some sufficient conditions for the existence of G-equivariant real frame fields on spheres with complementary G-equivariant complex structures are also obtained, improving earlier re...
On endomorphisms of surface mapping class groups Korkmaz, Mustafa (Elsevier BV, 2001-05-01) In this paper, we prove that every endomorphism of the mapping class group of an orientable surface onto a subgroup of finite index is in fact an automorphism.
On homotopy groups of real algebraic varieties and their complexifications Ozan, Yıldıray (Springer Science and Business Media LLC, 2004-10-01) Let X-0 be a topological component of a nonsingular real algebraic variety and i : X --> X-C is a nonsingular projective complexification of X. In this paper, we will study the homomorphism on homotopy groups induced by the inclusion map i: X-0 --> X-C and obtain several results using rational homotopy theory and other standard tools of homotopy theory.
Some upper bounds for density of function spaces Önal, Süleyman (Elsevier BV, 2009-05-01) Let C-alpha(X, Y) be the set of all continuous functions from X to Y endowed with the set-open topology where alpha is a hereditarily closed, compact network on X which is closed Under finite unions. We proved that the density of the space C-alpha(X, Y) is at most iw(X) . d(Y) where iw(X) denotes the i-weight of the Tychonoff space X, and d(Y) denotes the density of the space Y when Y is an equiconnected space with equiconnecting function psi, and Y has a base consists of psi-convex Subsets of Y. We also pr...
Legendrian knots and open book decompositions Çelik Onaran, Sinem; Korkmaz, Mustafa; Department of Mathematics (2009) In this thesis, we define a new invariant of a Legendrian knot in a contact manifold using an open book decomposition supporting the contact structure. We define the support genus of a Legendrian knot L in a contact 3-manifold as the minimal genus of a page of an open book of M supporting the contact structure such that L sits on a page and the framings given by the contact structure and the page agree. For any topological link in 3-sphere we construct a planar open book decomposition whose monodromy is a p...

Citation Formats

A. S. Demir, “On the algebraic structure of relative hamiltonian diffeomorphism group,” Ph.D. - Doctoral Program, Middle East Technical University, 2008.