On the algebraic structure of relative hamiltonian diffeomorphism group

Download
2008
Demir, Ali Sait
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.

Suggestions

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...
Some cardinal invariants on the space C-alpha (X, Y)
Onal, S; Vural, C (Elsevier BV, 2005-05-14)
Let C-alpha (X, Y) be the set of all continuous functions from X to Y endowed with the set-open topology where a is a hereditarily closed, compact network on X such that closed under finite unions. We define two properties (E1) and (E2) on the triple (alpha, X, Y) which yield new equalities and inequalities between some cardinal invariants on C-alpha (X, Y) and some cardinal invariants on the spaces X, Y such as:
Citation Formats
A. S. Demir, “On the algebraic structure of relative hamiltonian diffeomorphism group,” Ph.D. - Doctoral Program, Middle East Technical University, 2008.