Dehn functions of groups and extensions of complexes (Q1318501)

We study extensions of two-complexes and the Dehn functions (i.e. the isoperimetric inequalities) of their fundamental groups. If \(A \subset B\) are two complexes and their quotient \(X\) is diagrammatically and reducible then we obtain an upper bound for the Dehn function of \(\pi_ 1(B)\) in terms of the Dehn functions of \(\pi_ 1(A)\) and \(\pi_ 1(X)\). In particular, we show that if the Dehn functions of \(\pi_ 1(A)\) and \(\pi_ 1(X)\) are bounded above by polynomials of degree \(n\) and \(m\), then the Dehn function of \(\pi_ 1(B)\) is bounded above by a polynomial of degree \(n \cdot m\).