On the tight contact structures on seıfert fibred 3−manifolds with 4 singular fibers

Medetoğulları, Elif
In this thesis, we study the classification problem of Stein fillable tight contact structures on any Seifert fibered 3−manifold M over S 2 with 4 singular fibers. In the case e0(M) · −4 we have a complete classification. In the case e0(M) ¸ 0 we have obtained upper and lower bounds for the number of Stein fillable contact structures on M.


Exotic smooth structures on non-simply connected 4-manifolds
Topkara, Mustafa; Ozan, Yıldıray; Department of Mathematics (2010)
In this thesis, we study exotic smooth structures on 4-manifolds with finite fundamental groups. For an arbitrary finite group G, we construct an infinite family of smooth 4-manifolds with fundamental group G, which are all homeomorphic but mutually non-diffeomorphic, using the small symplectic manifold with arbitrary fundamental group constructed by S. Baldridge and P. Kirk, together with the methods of A. Akhmedov, R.Ý. Baykur and D. Park for constructing infinite families of exotic simply connected 4-man...
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.
On the algebraic structure of relative hamiltonian diffeomorphism group
Demir, Ali Sait; Ozan, Yıldıray; Department of Mathematics (2008)
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 Banyag...
The Investigation of Electronic, Elastic and Vibrational Properties of an Interlanthanide Perovskite: PrYbO3
The structural, mechanical, electronic and lattice dynamical properties of the PrYbO3 compound from the ABO(3)-type perovskite family have been investigated by performing the first-principles density functional theory calculations using the generalized-gradient approximation (GGA) with corrected Coulomb interactions (GGA+U). Structural parameters, formation energies and phase transition pressures for the five possible phases of this compound have been calculated. Then, the spin-dependent electronic band str...
Citation Formats
E. Medetoğulları, “On the tight contact structures on seıfert fibred 3−manifolds with 4 singular fibers,” Ph.D. - Doctoral Program, Middle East Technical University, 2010.