LEFSCHETZ PENCILS AND FINITELY PRESENTED GROUPS

摘要

From the works of Gompf and Donaldson, it is known that every finitely presented group can be realized as the fundamental group of the total space of a Lefschetz pencil. We give an alternative proof of this fact by providing the monodromy explicitly. In the proof, we give an alternative construction of the monodromy of Gurtas' fibration and a lift of that to the mapping class group of a surface with two boundary components.