Yörünge latisleri ve onların topolojileri

ABSTRACTTHE LATTICE OF PERIODS OF A GROUP ACTIONAND ITS TOPOLOGYHüseyin AcanuM.S. in MathematicsSupervisor: Asst. Prof. Dr. Ergün Yalşınu cJuly, 2006In this thesis, we study the topology of the poset obtained by removing thegreatest and least elements of lattice of periods of a group action. For a G-setX where G is a finite group, the lattice of periods is defined as the image of themap from the subgroup lattice of G to the partition lattice of X which sends asubgroup H of G to the partition of X whose blocks are the H-orbits of X. Westudy the homotopy type of the associated simplicial complex. When the groupG belongs to one of the families dihedral group of order 2n , dihedral group oforder 2pn where p is an odd prime, semi-dihedral group, or quaternion group andthe set X is transitive, we find the homotopy type of the corresponding poset. IfG is the dihedral group of order 2n or one of semidihedral and quaternion groups,we find that the homotopy type of the complex is either contractible or has thehomotopy type of three points. In the case of dihedral group of order 2pn , theassociated complex is either contractible or it has the homotopy type of p pointsor it has the homotopy type of p + 1 points.Keywords: lattice of periods, poset topology.i