Second order isoperimetric inequalities of split extensions. (Q1597754)

The second order Dehn function is an isoperimetric measure of the combinatorial complexity of the second homotopy module associated to a group presentation. It measures the maximal number of generators of the second homotopy module needed in order to generate pictures of given area. It is known that the second order Dehn function is a group invariant up to some equivalence relation for finitely presented groups with finitely generated second homotopy module. Wang studies the second order Dehn function of a split extension \(G\) of groups \(K\) and \(H\), where he assumes to know the second order Dehn functions of the factors. He writes down a finite set of generators of the second homotopy module of \(G\) by assuming such generators for \(K\) and \(H\). From this he achieves an upper bound of the second order Dehn function of \(G\) depending on the second order Dehn functions of the factors by drawing pictures of generators.