On solvable groups of knotted surfaces (Q1580381)

The group of a knotted surface (smooth, compact, connected, orientable) in 4-space is the fundamental group of its complement. Such a group is finitely presentable by Wirtinger relations, and is called an irreducible \(C\)-group by the author (dropping the finiteness condition). It is characterized as a group that is the normal closure of one element, has infinite cyclic abelianization and has a certain description of its second homology. This work investigates a natural category with \(C\)-groups as objects. \(C\)-normal subgroups, solvable and polycyclic \(C\)-groups are defined and their properties are studied. Polycyclic \(C\)-groups are characterized, and it is shown that they do occur as groups of 3-knots in 5-space in the finitely presented case.