The Fundamental group and methods of calculations

ABSTRACT Master of Science Thesis THE FUNDAMENTAL GROUP AND METHODS OF CALCULATIONS MURAT KOPARAN Anadolu University Graduate School of Natural and Applied Science Mathematics Program Supervisor: Assoc.Prof.Dr.Hüseyin AZCAN 2001, 31 pages In this study, the fundamental group and calculation methods were put forward. Homotopi map which allows us to form the structure of the fundamental group was described. It was proved that the fundamental groups of homeomorfic path-connected spaces were izomorfic. The fundamental group of simply connected spaces were calculated by giving orbit space definition. The fundamental group was calculated through the reading of generator and relations at G(K,L) group of path- connected triangulable spaces by defining G(K,L) group which was izomorfic to the edge group and the edge group of a complex. Finally, the example of fundamental group calculation was put forward by using Van Kampen Theorem. Keywords: Homotopy, Fundamental Group, Edge Group, Triangulable Space