Andrews-Curtis-Operationen und höhere kommutatoren der relatorengruppe

Abstract

AbstractIf K2 and L2 are compact, connected polyhedra of the same simple-homotopy type, then they can be 3-deformed to standard complexes of presentations with the same relator subgroup N⊆F(a1) and an equal number h of defining relators R1 resp. S1 such that R1S-11∈N (1), j = 1,…,h holds. It is shown in this paper that by applying further 3-deformations to one of the complexes, the quotients can be pushed up in the commutator series to become R1S-11∈ N(n). This is achieved by extending a method of W. Browning who treated presentations of perfect groups. The result is part of the authors' study of the Andrews-Curtis-problem