Lift Of 2-Complexes From Diagram Groups Over The Semigroup: Study Of Diagram Groups, Lift Of 2-Complexes, Extension Of Diagram Groups

Our interest in the new method to study of diagram groups, is motivated by kilibarda’s theorems (1994,1997), Guba and Sapir (1997). As the fundamental group isomorphism to diagram group, then it is easier than to work with fundamental groups instead of diagram groups. For any given semigroup presentation, we may obtain the 2- complexes of diagram groups. Using lifting method we would like to determine the specific generators, relations (2-cells), and spanning trees of 2-complexes from fundamental group.